Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “method of multipliers”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Asymptotic matching by the symbolic manipulator MACSYMA

The delegation of the labor of calculating higher-order terms in singular perturbation (SP) expansions to a computer by the use of MACSYMA is considered. The method of matched asymptotic expansions is studied in detail for two model SP problems: a model resembling the boundary layer equation with a small parameter multiplying the highest derivatives; and a turning-point problem. It is shown that MACSYMA has successfully performed the higher-order matching in both problems.

Lo, L. L.↗
DOE OSTI2020

Timing resolution and rate capability of Photonis miniPlanacon XPM85212/A1-S MCP-PMT

In this paper we report on a set of experiments that focus on measuring the timing performance of the Photonis miniPlanacon XPM85212/A1-S microchannel plate photomultiplier tubes along with the detector response at high event rates. The detector has a single photoelectron timing resolution of 30 ps at low rates ( 10 kHz ). We show that both the gain and the timing start to deteriorate around 1 MHz with 20 photoelectrons per channel at 1 0 4 target gain, giving the current per unit of area limits of 1.38 μ A / cm 2 and 2.38 μ A / cm 2 for the two tested devices. Photo-multiplier tubes with lower micro-channel plate resistivity exhibit a better rate capability due to the faster replenishment of the charge inside the microchannels. As we demonstrate, another method to improve the rate capability is to operate the photon detector tubes at a lower gain by reducing the supply voltage and compensating for the loss of amplitude by an additional amplification stage at the expense of the achieved timing resolution. The tube active area over which the beam is spread also plays a role since the same amount of light yields a better rate capability when spread over a larger area. The tubes exposed to high event rates showed an uncharacteristically slow recovery back to its initial gain with 80 % of the initial gain recovered only after several tens of minutes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Variational, stable, and self-consistent coupling of 3D electromagnetics to 1D transmission lines in the time domain

This work presents a new multiscale method for coupling the 3D Maxwell's equations to the 1D telegrapher's equations. While Maxwell's equations are appropriate for modeling complex electromagnetics in arbitrary-geometry domains, simulation cost for many applications (e.g. pulsed power) can be dramatically reduced by representing less complex transmission line regions of the domain with a 1D model. By assuming a transverse electromagnetic (TEM) ansatz for the solution in a transmission line region, we reduce the Maxwell's equations to the telegrapher's equations. Here, we propose a self-consistent finite element formulation of the fully coupled system that uses boundary integrals to couple between the 3D and 1D domains and supports arbitrary unstructured 3D meshes. Additionally, by using a Lagrange multiplier to enforce continuity at the coupling interface, we allow for an absorbing boundary condition to also be applied to non-TEM modes on this boundary. We demonstrate that this feature reduces non-physical reflection and ringing of non-TEM modes off of the coupling boundary. By employing implicit time integration, we ensure a stable coupling, and we introduce an efficient method for solving the resulting linear systems. We demonstrate the accuracy of the new method on two verification problems, a transient O-wave in a rectilinear prism and a steady-state problem in a coaxial geometry, and show the efficiency and weak scalability of our implementation on a cold test of the Z-machine MITL and post-hole convolute.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1982

Sensitivity of constrained linear inversions to the selection of the Lagrange multiplier

The influence of the choice of the Lagrange multiplier on constrained linear inversions is explored, with reference made to applications in inferring the columnar aerosol size distributions from spectral aerosol optical depth measurements. A range of the Lagrange multiplier is examined to find all positive solutions for the solution vector, which represents modifying factors to the assumed form of the size distribution. An iterative method is devised to constrain the calculations to consideration of only positive quantities and a requirement that the regression fit to data be consistent with measurement errors. The determination of the variances and covariances is formulated and applied to existing data sets for optical depth. Variances in the solution are found to be large for particle radii when the information content of the data is small.

King, M. D.↗
NASA NTRS1982

Mass motions in the solar chromosphere and transition zone

A comparison is made between H-alpha and C IV observations of Active Region 2717 on October 9, 1980. On the basis of this comparison, it is found that upward velocities are present above sunspots in the chromosphere-corona transition zone (20 km/s). The downward velocities are found to be well correlated in both lines. Doppler-shift ratios between C IV and H-alpha levels (approximately 10) are seen to be much smaller than expected from density ratio estimates. The comparison is seen as suggesting that flow lines are probably far from vertical in the transition zone. It is pointed out, however, that this depends on model densities that may not be correct. A simple method for comparing matter flows is presented. The best fit between H-alpha and C IV levels is obtained when C IV Doppler shifts are multiplied by the line intensity to the power 0.5 (approximately) in order to make allowance for density fluctuations.

Mein, P.↗
DOE OSTI2023

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. Furthermore, we also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Axisymmetric solid elements by a rational hybrid stress method

Four-node axisymmetric solid elements are derived by a new version of hybrid method for which the assumed stresses are expressed in complete polynomials in natural coordinates. The stress equilibrium conditions are introduced through the use of additional displacements as Lagrange multipliers. A rational procedure is to choose the displacement terms such that the resulting strains are also of complete polynomials of the same order. Example problems all indicate that elements obtained by this procedure lead to better results in displacements and stresses than that by other finite elements.

Tian, Z.↗
NASA NTRS1990

Performance analysis of structured gradient algorithm

The structured gradient algorithm uses a structured estimate of the array correlation matrix (ACM) to estimate the gradient required for the constrained least-mean-square (LMS) algorithm. This structure reflects the structure of the exact array correlation matrix for an equispaced linear array and is obtained by spatial averaging of the elements of the noisy correlation matrix. In its standard form the LMS algorithm does not exploit the structure of the array correlation matrix. The gradient is estimated by multiplying the array output with the receiver outputs. An analysis of the two algorithms is presented to show that the covariance of the gradient estimated by the structured method is less sensitive to the look direction signal than that estimated by the standard method. The effect of the number of elements on the signal sensitivity of the two algorithms is studied.

Godara, Lal C.↗
NASA NTRS1994

Multigrid one shot methods for optimal control problems: Infinite dimensional control

The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

Arian, Eyal↗
DOE OSTI2021

Analysis of Lobe Power Calculator and Indication System with Physics and Cycle Based Models

The Advanced Test Reactor (ATR) at INL measures reactor power through two methods, thermal and Nitrogen-16 (N-16) activity. Water power calculator (WPC) is a thermal power system that measures flow and temperature to determine the thermal quadrant powers. The N-16 system utilizes a beta chamber detector that outputs reactivity levels to calculate lobe power through an algorithm called lobe power calculation and indication system (LPCIS). The LPCIS utilizes the N-16 system and the WPC system to determine reactor core power levels. The WPC provides accurate calculations of quadrant and total reactor thermal power. With the use of WPC measurements, thermal-to-N-16 (T2N) power ratios are produced to determine if the two indication systems agree on core power. Relative magnitude equations are used to utilize N-16 coefficients and multipliers to improve the indications of the LPCIS. This is crucial for maintaining safety limits. Currently, the LPCIS system uses linear equations and matrices to calculate lobe power through multipliers and coefficients. Advancements in technology and system upgrades have assisted system engineers at INL with the objective to reach a more dynamic system. In return the system demonstrates an increase in the accuracy of power reading while maintaining safety margins. The new proposed coefficient and multiple method implements a cycle specific, and a physics-based model intended for changing coefficients during operation. This calibration experiment focuses on power splitting, outer shim and neck shim, as well as fuel burning into the RDAS weighting factors. Results show that the Physics learning method yields a smaller error margin inside of the desired power range for the data set 166-A. This proved true for both constrained and unconstrained testing. This is most likely due to the physics data fitting approach that resulted in favorable coefficients and multipliers for 166-A. Continuing to improve the physics-based model will help improve the power accuracy of the LPCIS system.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Recent Improvements to the NWChem COSMO Module

This work presents recent developments in the COSMO solvation model implementation in NWChem. A new cavity construction approach, based on the solvent-excluding surface (SES) and utilizing the well-established GEPOL algorithm, has been introduced. Additionally, a straightforward procedure to merge surface segments that are too close─often a source of numerical artifacts─has been implemented. The available methods for correcting outlying surface charges have also been reviewed and improved. To validate the new implementation, we computed dielectric solvation energies for a chemically diverse set of approximately 100 molecules, including neutral species, small ions, and common ionic liquid components. Results were compared to those from GAMESS using the double-cavity method as a reference. Although the double-cavity approach can be regarded as more accurate, the simpler correction schemes available in NWChem─based on scaling factors or Lagrange multipliers─can achieve excellent agreement if the potential is also properly corrected, with mean unsigned deviations of around 0.15 kcal/mol. Predictions of typical vapor–liquid and liquid–liquid equilibria using a COSMO-SAC variant based on NWChem also showed very promising results.

Cavities↗
NASA NTRS1975

Dynamic analysis of the GEOS satellite

The assumed modes method is used to investigate the stability of the GEOS satellite. The system is discretized by representing the continuous displacement by finite series of space-dependent admissible functions multiplied by time-dependent generalized coordinates. The spatial dependence is eliminated by integration over the elastic domains, so that the testing functional reduces to a testing function. The sign properties of the testing function are then tested and the equilibrium defined as nontrivial. In considering the stability of small motions about nontrivial equilibrium, it is shown that if the analysis performed by ignoring the motion of the mass center indicates stability, then the system remains stable if the motion of the mass center is included.

Meirovitch, L.↗
NASA NTRS1992

Unsteady incompressible flow computations with the finite-element method

While the methods thus far developed for vorticity-streamfunction formulation are thus far restricted to 2D flows, they are applicable to both viscous and inviscid flows, including problems with multiply-connected domains. The present solution techniques for the velocity-pressure formulation can be extended to 3D problems. Attention is given to (1) two multistep formulations that use piecewise bilinear functions for the velocity and piecewise constant functions for the pressure, and (2) a novel multistep velocity-pressure formulation based on the equal-order interpolation of velocity and pressure.

Tezduyar, T. E.↗
NASA NTRS2004

A Survey of Formal Methods for Intelligent Swarms

Swarms of intelligent autonomous spacecraft, involving complex behaviors and interactions, are being proposed for future space exploration missions. Such missions provide greater flexibility and offer the possibility of gathering more science data than traditional single spacecraft missions. The emergent properties of swarms make these missions powerful, but simultaneously far more difficult to design, and to assure that the proper behaviors will emerge. These missions are also considerably more complex than previous types of missions, and NASA, like other organizations, has little experience in developing or in verifying and validating these types of missions. A significant challenge when verifying and validating swarms of intelligent interacting agents is how to determine that the possible exponential interactions and emergent behaviors are producing the desired results. Assuring correct behavior and interactions of swarms will be critical to mission success. The Autonomous Nano Technology Swarm (ANTS) mission is an example of one of the swarm types of missions NASA is considering. The ANTS mission will use a swarm of picospacecraft that will fly from Earth orbit to the Asteroid Belt. Using an insect colony analogy, ANTS will be composed of specialized workers for asteroid exploration. Exploration would consist of cataloguing the mass, density, morphology, and chemical composition of the asteroids, including any anomalous concentrations of specific minerals. To perform this task, ANTS would carry miniaturized instruments, such as imagers, spectrometers, and detectors. Since ANTS and other similar missions are going to consist of autonomous spacecraft that may be out of contact with the earth for extended periods of time, and have low bandwidths due to weight constraints, it will be difficult to observe improper behavior and to correct any errors after launch. Providing V&V (verification and validation) for this type of mission is new to NASA, and represents the cutting edge in system correctness, and requires higher levels of assurance than other (traditional) missions that use a single or small number of spacecraft that are deterministic in nature and have near continuous communication access. One of the highest possible levels of assurance comes from the application of formal methods. Formal methods are mathematics-based tools and techniques for specifying and verifying (software and hardware) systems. They are particularly useful for specifying complex parallel systems, such as exemplified by the ANTS mission, where the entire system is difficult for a single person to fully understand, a problem that is multiplied with multiple developers. Once written, a formal specification can be used to prove properties of a system (e.g., the underlying system will go from one state to another or not into a specific state) and check for particular types of errors (e.g., race or livelock conditions). A formal specification can also be used as input to a model checker for further validation. This report gives the results of a survey of formal methods techniques for verification and validation of space missions that use swarm technology. Multiple formal methods were evaluated to determine their effectiveness in modeling and assuring the behavior of swarms of spacecraft using the ANTS mission as an example system. This report is the first result of the project to determine formal approaches that are promising for formally specifying swarm-based systems. From this survey, the most promising approaches were selected and are discussed relative to their possible application to the ANTS mission. Future work will include the application of an integrated approach, based on the selected approaches identified in this report, to the formal specification of the ANTS mission.

Truszkowski, Walt↗
NASA NTRS1980

Method and apparatus for quadriphase-shift-key and linear phase modulation

A submultiple of an S-band transmitter output frequency was divided equally between a linear phase modulation branch and a QPSK modulation branch. The linear modulation branch includes a multiplier to increase the carrier frequency to a level which, when combined with the carrier in the QPSK branch in an up-converter (utilizing a mixer at the input followed by a bandpass filter), produces the transmitter output frequency. This allows the QPSK modulator to operate at one-eighth of the output frequency where repeatable and precisely controlled modulation can be easily achieved. This also allows linear phase modulation at one-eighth the output frequency where low modulator deviation and good linearity can be easily maintained.

Hermesmeyer, C. E.↗
DOE OSTI2021

In crystallo organometallic chemistry

X-ray crystallography is an invaluable tool in design and development of organometallic catalysis, but application typically requires species to display sufficiently high solution concentrations and lifetimes for single crystalline samples to be obtained. In crystallo organometallic chemistry relies on chemical reactions that proceed within the single-crystal environment to access crystalline samples of reactive organometallic fragments that are unavailable by alternate means. Furthermore, this highlight describes approaches to in crystallo organometallic chemistry including (a) solid–gas reactions between transition metal complexes in molecular crystals and diffusing small molecules, (b) reactions of organometallic complexes within the extended lattices of metal–organic frameworks (MOFs), and (c) intracrystalline photochemical transformations to generate reactive organometallic fragments. Application of these methods has enabled characterization of catalytically important transient species, including σ-alkane adducts of transition metals, metal alkyl intermediates implicated in metal-catalyzed carbonylations, and reactive M–L multiply bonded species involved in C–H functionalization chemistry. Opportunities and challenges for in crystallo organometallic chemistry are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Efficient Scalable Contact Network Generation from Population Data

Modeling the contacts among a population is critical to understanding the dynamics of a disease outbreak. Contact networks, where nodes are individuals and edges are contacts among them, are used to represent these complex individual-level interactions. In this work, we are given the daily activity schedules of an urban population that represent the activity location and time of individuals in a population during a single twenty four hour period over multiple days. Using collocation to determine contact between individuals, our goal is to extract hourly contact networks from large-scale activity data. We improve upon the existing adjacency matrix-based method by implementing our custom sparse matrix multiplication algorithm. Starting with a Python implementation, we achieve a 1600x speed up in the computation with a fast custom designed sparse matrix multiplier algorithm implemented in the C++ language. This work is central to future parallel designs of the problem.

97 MATHEMATICS AND COMPUTING↗