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All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Fast Bound Methods for Large Scale Simulation with Application for Engineering Optimization

In this work, we have focused on fast bound methods for large scale simulation with application for engineering optimization. The emphasis is on the development of techniques that provide both very fast turnaround and a certificate of Fidelity; these attributes ensure that the results are indeed relevant to - and trustworthy within - the engineering context. The bound methodology which underlies this work has many different instantiations: finite element approximation; iterative solution techniques; and reduced-basis (parameter) approximation. In this grant we have, in fact, treated all three, but most of our effort has been concentrated on the first and third. We describe these below briefly - but with a pointer to an Appendix which describes, in some detail, the current "state of the art."

Patera, Anthony T.↗
NASA NTRS2002

Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods

We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced basis approximations, Galerkin projection onto a space W(sub N) spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation, relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures, methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage, in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.

Prudhomme, C.↗
NASA NTRS2002

Bounding the Risk of Crew Loss Following Orbital Debris Penetration of the International Space Station at Assembly Stages 1J and 1E

Orbital debris impacts on the International Space Station occur frequently. To date, none of the impacting particles has been sufficiently large to penetrate manned pressurized volumes. We used the Manned Spacecraft Crew Survivability code to evaluate the risk to crew of penetrations of pressurized modules at two assembly stages: after Flight lJ, when the pressurized elements of Kibo, the Japanese Experiment Module, are present, and after Flight lE, when the European Columbus Module is present. Our code is a Monte Carlo simulation of impacts on the Station that considers several potential event types that could lead to crew loss. Among the statistics tabulated by the program is the probability of death of one or more crew members, expressed as the risk factor, R. This risk factor is dependent on details of crew operations during both ordinary circumstances and decompression emergencies, as well as on details of internal module configurations. We conducted trade studies considering these procedure and configuration details to determine the bounds on R at the 1J and 1E stages in the assembly sequence. Here we compare the R-factor bounds, and procedures and configurations that reduce R at these stages.

Evans, S.↗
NASA NTRS1988

Evidence against the involvement of ionically bound cell wall proteins in pea epicotyl growth

Ionically bound cell wall proteins were extracted from 7 day old etiolated pea (Pisum sativum L. cv Alaska) epicotyls with 3 molar LiCl. Polyclonal antiserum was raised in rabbits against the cell wall proteins. Growth assays showed that treatment of growing region segments (5-7 millimeters) of peas with either dialyzed serum, serum globulin fraction, affinity purified immunoglobulin, or papain-cleaved antibody fragments had no effect on growth. Immunofluorescence microscopy confirmed antibody binding to cell walls and penetration of the antibodies into the tissues. Western blot analysis, immunoassay results, and affinity chromatography utilizing Sepharose-bound antibodies confirmed recognition of the protein preparation by the antibodies. Experiments employing in vitro extension as a screening measure indicated no effect upon extension by antibodies, by 50 millimolar LiCl perfusion of the apoplast or by 3 molar LiCl extraction. Addition of cell wall protein to protease pretreated segments did not restore extension nor did addition of cell wall protein to untreated segments increase extension. It is concluded that, although evidence suggests that protein is responsible for the process of extension, the class(es) of proteins which are extracted from pea cell walls with 3 molar LiCl are probably not involved in this process.

NASA Program Space Biology↗
NASA NTRS1997

Computation of LFT Uncertainty Bounds with Repeated Parametric Uncertainties

A new methodology in which linear fractional transformation uncertainty bounds are directly constructed for use in robust control design and analysis is proposed. Existence conditions for model validating solutions with or without repeated scalar uncertainty are given. The approach is based on minimax formulation to deal with multiple non-repeated structured uncertainty components subject to fixed levels of repeated scalar uncertainties. Input directional dependence and variations with different experiments are addressed by maximizing uncertainty levels over multiple experimental data sets. Preliminary results show that reasonable uncertainty bounds on structured non-repeated uncertainties can be identified directly from measurement data by assuming reasonable levels of repeated scalar uncertainties.

Lim, K. B.↗
NASA NTRS1989

Purification and characterization of soluble (cytosolic) and bound (cell wall) isoforms of invertases in barley (Hordeum vulgare) elongating stem tissue

Three different isoforms of invertases have been detected in the developing internodes of barley (Hordeum vulgare). Based on substrate specificities, the isoforms have been identified to be invertases (beta-fructosidases EC 3.2.1.26). The soluble (cytosolic) invertase isoform can be purified to apparent homogeneity by diethylaminoethyl cellulose, Concanavalin-A Sepharose, organo-mercurial Sepharose, and Sephacryl S-300 chromatography. A bound (cell wall) invertase isoform can be released by 1 molar salt and purified further by the same procedures as above except omitting the organo-mercurial Sepharose affinity chromatography step. A third isoform of invertase, which is apparently tightly associated with the cell wall, cannot be isolated yet. The soluble and bound invertase isoforms were purified by factors of 60- and 7-fold, respectively. The native enzymes have an apparent molecular weight of 120 kilodaltons as estimated by gel filtration. They have been identified to be dimers under denaturing and nondenaturing conditions. The soluble enzyme has a pH optimum of 5.5, Km of 12 millimolar, and a Vmax of 80 micromole per minute per milligram of protein compared with cell wall isozyme which has a pH optimum of 4.5, Km of millimolar, and a Vmax of 9 micromole per minute per milligram of protein.

NASA Program Space Biology↗
NASA NTRS1999

Cross-linking staphylococcal enterotoxin A bound to major histocompatibility complex class I is required for TNF-alpha secretion

The mechanism of how superantigens function to activate cells has been linked to their ability to bind and cross-link the major histocompatibility complex class II (MHCII) molecule. Cells that lack the MHCII molecule also respond to superantigens, however, with much less efficiency. Therefore, the purpose of this study was to confirm that staphylococcal enterotoxin A (SEA) could bind the MHCI molecule and to test the hypothesis that cross-linking SEA bound to MHCII-deficient macrophages would induce a more robust cytokine response than without cross-linking. We used a capture enzyme-linked immunosorbent assay and an immunprecipitation assay to directly demonstrate that MHCI molecules bind SEA. Directly cross-linking MHCI using monoclonal antibodies or cross-linking bound SEA with an anti-SEA antibody or biotinylated SEA with avidin increased TNF-alpha and IL-6 secretion by MHCII(-/-) macrophages. The induction of a vigorous macrophage cytokine response by SEA/anti-SEA cross-linking of MHCI offers a mechanism to explain how MHCI could play an important role in superantigen-mediated pathogenesis. Copyright 1999 Academic Press.

NASA Discipline Musculoskeletal↗
NASA NTRS2005

Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all red-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principle formulation of bounded rationality and a set of new types of mean field theory in statistical physics; it also shows that those topics are fundamentally one and the same.

Wolpert, David H.↗
NASA NTRS2004

Bounding the risk of crew loss following orbital debris penetration of the International Space Station at assembly stages 1J and 1E

Orbital debris impacts on the International Space Station occur frequently. To date, none of the impacting particles has been large enough to penetrate manned pressurized volumes. We used the Manned Spacecraft Crew Survivability code to evaluate the risk to crew of penetrations of pressurized modules at two assembly stages: after Flight 1J, when the pressurized elements of Kibo, the Japanese Experiment Module, are present, and after Flight 1E, when the European Columbus Module is present. Our code is a Monte-Carlo simulation of impacts on the Station that considers several potential event types that could lead to crew loss. Among the statistics tabulated by the program is the probability of death of one or more crew members in the event of a penetration, expressed as the risk factor, R. This risk factor is dependent on details of crew operations during both ordinary circumstances and decompression emergencies, as well as on details of internal module configurations. We conducted trade studies considering these procedure and configuration details to determine the bounds on R at the 1J and 1E stages in the assembly sequence. Here we compare the R-factor bounds, and procedures could that reduce R at these stages. Published by Elsevier Ltd on behalf of COSPAR.

Models, Theoretical↗
NASA NTRS1994

Improved Bounds on Non-Luminous Matter in Solar Orbit

We improve, using a larger set of observations including Voyager 2 Neptune flyby data, previous bounds on the amount of dark matter (DM) trapped in a spherically symmetric distribution about the sun. We bound DM by noting that such a distribution would increase the effective mass of the sun as seen by the outer planets and by finding the uncertainty in that effective mass for Uranus and Neptune in fits to the JPL Developmental Ephermeris residuals, including optical data and those two planets' Voyager 2 flybys. We extend our previous procedure by fitting more parameters of the developmental ephemerides. Additionally, we present here the values for Pioneer 10 and 11 and Voyager 1 and 2 Jupiter ranging normal points (and incorporate these data as well).

dark matter Deep Space Network DSN Voyager Neptune↗
NASA NTRS2009

Analytic Confusion Matrix Bounds for Fault Detection and Isolation Using a Sum-of-Squared- Residuals Approach

Given a system which can fail in 1 or n different ways, a fault detection and isolation (FDI) algorithm uses sensor data in order to determine which fault is the most likely to have occurred. The effectiveness of an FDI algorithm can be quantified by a confusion matrix, which i ndicates the probability that each fault is isolated given that each fault has occurred. Confusion matrices are often generated with simulation data, particularly for complex systems. In this paper we perform FDI using sums of squares of sensor residuals (SSRs). We assume that the sensor residuals are Gaussian, which gives the SSRs a chi-squared distribution. We then generate analytic lower and upper bounds on the confusion matrix elements. This allows for the generation of optimal sensor sets without numerical simulations. The confusion matrix bound s are verified with simulated aircraft engine data.

Simon, Dan↗
NASA NTRS2014

Bifurcation Analysis Using Rigorous Branch and Bound Methods

For the study of nonlinear dynamic systems, it is important to locate the equilibria and bifurcations occurring within a specified computational domain. This paper proposes a new approach for solving these problems and compares it to the numerical continuation method. The new approach is based upon branch and bound and utilizes rigorous enclosure techniques to yield outer bounding sets of both the equilibrium and local bifurcation manifolds. These sets, which comprise the union of hyper-rectangles, can be made to be as tight as desired. Sufficient conditions for the existence of equilibrium and bifurcation points taking the form of algebraic inequality constraints in the state-parameter space are used to calculate their enclosures directly. The enclosures for the bifurcation sets can be computed independently of the equilibrium manifold, and are guaranteed to contain all solutions within the computational domain. A further advantage of this method is the ability to compute a near-maximally sized hyper-rectangle of high dimension centered at a fixed parameter-state point whose elements are guaranteed to exclude all bifurcation points. This hyper-rectangle, which requires a global description of the bifurcation manifold within the computational domain, cannot be obtained otherwise. A test case, based on the dynamics of a UAV subject to uncertain center of gravity location, is used to illustrate the efficacy of the method by comparing it with numerical continuation and to evaluate its computational complexity.

Smith, Andrew P.↗
NASA NTRS2015

An Upper Bound on High Speed Satellite Collision Probability When Only One Object has Position Uncertainty Information

Upper bounds on high speed satellite collision probability, PC †, have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum PC. If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but potentially useful Pc upper bound.

Frisbee, Joseph H., Jr.↗
NASA NTRS2015

Uncertainty Quantification of Turbulence Model Closure Coefficients for Transonic Wall-Bounded Flows

The goal of this work was to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients was performed for transonic flow over an axisymmetric bump at zero degrees angle of attack and the RAE 2822 transonic airfoil at a lift coefficient of 0.744. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) k-w Model, and the Menter Shear-Stress Trans- port Model. The FUN3D code developed by NASA Langley Research Center was used as the flow solver. The uncertainty quantification analysis employed stochastic expansions based on non-intrusive polynomial chaos as an efficient means of uncertainty propagation. Several integrated and point-quantities are considered as uncertain outputs for both CFD problems. All closure coefficients were treated as epistemic uncertain variables represented with intervals. Sobol indices were used to rank the relative contributions of each closure coefficient to the total uncertainty in the output quantities of interest. This study identified a number of closure coefficients for each turbulence model for which more information will reduce the amount of uncertainty in the output significantly for transonic, wall-bounded flows.

Schaefer, John↗
NASA NTRS2020

Implicit Formulations of Bounded-Impulse Trajectory Models for Preliminary Interplanetary Low-Thrust Analysis

The bounded-impulse approach to low-thrust interplanetary trajectory optimization is widely used. In an effort to efficiently implement this approach using NASA’s OpenMDAO optimization software, the authors have implemented implicit formulations of the forward shooting/backwards-shooting methods commonly used in bounded-impulse models. These implicit approaches allow for vectorization of the underlying calculations which can significantly reduce runtime in interpreted languages. An implicit approach may be either converged by using an underlying nonlinear solver to converge the state propagation, or as a constraint in an optimizer-driven multiple-shooting approach. Significant computational efficiency gains are realized through the utilization of the modular approach to unified derivatives. Further computational efficiency is achieved by capitalizing on the sparsity of the constraint Jacobian matrix. This work demonstrates that a vectorized multiple-shooting approach for propagating a state-time history is superior in terms of computational efficiency as the number of segments in the state-propagation is increased.

Falck, Robert D↗
NASA NTRS2022

Ultraviolet Photooxidation of Smectite-Bound Fe(II) and Implications for the Origin of Martian Nontronites

Clay minerals detected with orbital and in situ instruments in ancient Martian terrains constrain Mars' climate and aqueous alteration history. Early in its history, Mars experienced an atmospheric redox change and iron-bearing clay minerals may preserve the effects of that transition. Ferrous smectites, the thermodynamically predicted product of chemical weathering of basalts under anoxic conditions, may have undergone oxidation by exposure to chemical oxidants in the atmosphere or regolith, or by direct photooxidation at the surface. To assess these potential oxidation pathways, ferrous trioctahedral smectites of varying initial iron content were synthesized and subjected to oxidation by ultraviolet (UV) irradiation. Experimental UV irradiation under an anoxic atmosphere equivalent to approximately 7 years of flux on the Martian surface caused partial oxidation of smectite-bound Fe (Fe3+/ΣFe = 16–18%) and octahedral sheet contraction. Metal-OH vibrational bands in visible/near infrared (VNIR) reflectance spectra of oxidized smectites changed in band depth and asymmetry with higher iron content. X-ray diffraction patterns of UV irradiated samples indicate the formation of a mixed di- and trioctahedral smectite or a secondary nontronite phase, possibly on the surfaces of higher iron content smectites. These experiments suggest that UV irradiation is able to oxidize structurally bound iron in smectites without the presence of other chemical oxidants. Photooxidation may have influenced the mineralogy, both syndepositionally and postdepositionally, of Martian alteration assemblages formed near the surface and this process needs not be limited to one part of their formation history. Plain Language Summary: Martian mineral assemblages observed with orbiters and rover instruments allow us to understand the planet's past climate and aqueous activity. Hydrated minerals that contain Fe(II) are of particular interest as they would have been affected by the early atmosphere becoming more oxidizing overtime, changing the structural iron into Fe(III). In this study, we synthesized Fe(II) smectites with varying iron content and irradiated them with an ultraviolet (UV) light source to test whether they could be photooxidized. Iron in the smectite minerals was incompletely oxidized by UV radiation after being exposed for the equivalent of approximately 7 years of exposure on the early Mars surface. The smectites with higher iron content showed more changes with photooxidation in their visible/near infrared spectra as well as in their X-ray diffraction patterns, two datasets collected by instruments on currently active Martian missions. These results suggest that UV photooxidation is a plausible contributor to the mineralogy and redox state of clay mineral assemblages observed at the Martian surface.

V. B. Rivera Banuchi↗
NASA NTRS2024

Under-Constrained SEE Data: Implications for Estimating and Bounding SEE Rates

Increasingly scarce SEE testing resources and rapid growth of the New Space sector have increased the prevalence of under-constrained SEE data. We develop Monte Carlo tools to assess implications for SEE rate estimation. We also show that Bayesian Priors based on large datasets of SEL susceptible parts can augment under-constrained data and improve bounds on SEL rates. The resulting Bayesian Priors are also useful for bounding system SEL risk.

Single-event effect↗
DOE OSTI2020

Quantum information processing with majorana bound states in superconducting circuits

In a weak link of two s-wave superconductors (SCs) coupled via a time-reversal-invariant (TRI) topological superconducting (TSC) island, a Josephson current can flow due to Cooper pairs tunneling in and out of spatially separated Majorana Kramers pairs (MKPs), which are doublets of Majorana bound states (MBSs). The sign of the resulting Josephson current is fixed by the joint parity of the four Majorana bound states that make up the MKPs on the TSC island. This parity-controlled Josephson effect can be used as a read-out mechanism for the joint parity in Majorana-based quantum computing. For a TSC island with four terminals, the SC leads can address a Majorana superconducting qubit (MSQ) formed by the charge ground states of the TSC island's terminals. Cooper pair splitting enables single-qubit operations, qubit read-out, as well as two-qubit entangling gates. Hence, TSC islands between SC leads may provide an alternative approach to superconducting quantum computation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗