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NASA NTRS1994

Thermodynamic models for bounding pressurant mass requirements of cryogenic tanks

Thermodynamic models have been formulated to predict lower and upper bounds for the mass of pressurant gas required to pressurize a cryogenic tank and then expel liquid from the tank. Limiting conditions are based on either thermal equilibrium or zero energy exchange between the pressurant gas and initial tank contents. The models are independent of gravity level and allow specification of autogenous or non-condensible pressurants. Partial liquid fill levels may be specified for initial and final conditions. Model predictions are shown to successfully bound results from limited normal-gravity tests with condensable and non-condensable pressurant gases. Representative maximum collapse factor maps are presented for liquid hydrogen to show the effects of initial and final fill level on the range of pressurant gas requirements. Maximum collapse factors occur for partial expulsions with large final liquid fill fractions.

Vandresar, Neil T.↗
NASA NTRS1991

Modifications of the Griesmer bound

The Griesmer bound is a classical technique (developed in 1960) for estimating the minimum length n required for a binary linear code with a given dimension k and minimum distance d. In this article, a unified derivation of the Griesmer bound and two new variations on it are presented. The first variation deals with linear codes which contain the all-ones vector; such codes are quite common and are useful in practice because of their 'transparent' properties. The second variation deals with codes that are constrained to contain a word of weight greater than or equal to M. In both cases these constraints (the all-ones word or a word of high weight) can increase the minimum length of a code with given k and d.

Mceliece, R. J.↗
NASA NTRS1995

Estimating the Cramer-Rao bound for restored astronomical observations

This work addresses the problem of assigning confidence intervals to estimated photometry data obtained from astronomical observations. The proposed solution is to estimate the Cramer-Rao bound, which is an analytical expression that describes the minimum obtainable mean square error associated with a given estimate of a parameter. This Letter presents a compact and simple form for the bound associated with a linear estimator such as a Wiener filter estimator. A prescription for estimating the variance associated with each element in a restored object was developed using an analytical model for observed data corrupted by either Poisson or Gaussian noise. Both one- and two-dimensional examples are presented.

Zaccheo, T. S.↗
NASA NTRS1996

Bounds on Block Error Probability for Multilevel Concatenated Codes

Maximum likelihood decoding of long block codes is not feasable due to large complexity. Some classes of codes are shown to be decomposable into multilevel concatenated codes (MLCC). For these codes, multistage decoding provides good trade-off between performance and complexity. In this paper, we derive an upper bound on the probability of block error for MLCC. We use this bound to evaluate difference in performance for different decompositions of some codes. Examples given show that a significant reduction in complexity can be achieved when increasing number of stages of decoding. Resulting performance degradation varies for different decompositions. A guideline is given for finding good m-level decompositions.

Lin, Shu↗
NASA NTRS1996

A study of the turbulence structures of wall-bounded shear flows

This project extends the study of the structure of wall-bounded flows using the topological properties of eddying motions as developed by Chong et al. (1990), Soria et al. (1992, 1994), and as recently extended by Blackburn et al. (1996) and Chacin et al. (1996). In these works, regions of flow which are focal in nature are identified by being enclosed by an isosurface of a positive small value of the discriminant of the velocity gradient tensor. These regions resemble the attached vortex loops suggested first by Theodorsen (1955). Such loops are incorporated in the attached eddy model versions of Perry & Chong (1982), Perry et al. (1986), and Perry & Marusic (1995), which are extensions of a model first formulated by Townsend (1976). The DNS data of wall bounded flows studied here are from the zero pressure gradient flow of Spalart (1988) and the boundary layer with separation and reattachment of Na & Moin (1996). The flow structures are examined from the viewpoint of the attached eddy hypothesis.

Chong, M. S.↗
NASA NTRS1994

A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization

When a classical barrier method is applied to the solution of a nonlinear programming problem with inequality constraints, the Hessian matrix of the barrier function becomes increasingly ill-conditioned as the solution is approached. As a result, it may be desirable to consider alternative numerical algorithms. We compare the performance of two methods motivated by barrier functions. The first is a stabilized form of the classical barrier method, where a numerically stable approximation to the Newton direction is used when the barrier parameter is small. The second is a modified barrier method where a barrier function is applied to a shifted form of the problem, and the resulting barrier terms are scaled by estimates of the optimal Lagrange multipliers. The condition number of the Hessian matrix of the resulting modified barrier function remains bounded as the solution to the constrained optimization problem is approached. Both of these techniques can be used in the context of a truncated-Newton method, and hence can be applied to large problems, as well as on parallel computers. In this paper, both techniques are applied to problems with bound constraints and we compare their practical behavior.

Nash, Stephen G.↗
NASA NTRS1997

Locating the Discontinuities of a Bounded Function by the Partial Sums of its Fourier Series I: Periodical Case

A key step for some methods dealing with the reconstruction of a function with jump discontinuities is the accurate approximation of the jumps and their locations. Various methods have been suggested in the literature to obtain this valuable information. In the present paper, we develop an algorithm based on identities which determine the jumps of a 2(pi)-periodic bounded not-too-highly oscillating function by the partial sums of its differentiated Fourier series. The algorithm enables one to approximate the locations of discontinuities and the magnitudes of jumps of a bounded function. We study the accuracy of approximation and establish asymptotic expansions for the approximations of a 27(pi)-periodic piecewise smooth function with one discontinuity. By an appropriate linear combination, obtained via derivatives of different order, we significantly improve the accuracy. Next, we use Richardson's extrapolation method to enhance the accuracy even more. For a function with multiple discontinuities we establish simple formulae which "eliminate" all discontinuities of the function but one. Then we treat the function as if it had one singularity following the method described above.

Kvernadze, George↗
NASA NTRS1998

A Posteriori Finite Element Bounds for Sensitivity Derivatives of Partial-Differential-Equation Outputs

We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, 'constant-free' upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori finite element procedure is described; the asymptotic bounding properties and computational complexity of the method are summarized; and illustrative numerical results are presented.

Lewis, Robert Michael↗
NASA NTRS1995

The Topographic Torque on a Bounding Surface of a Rotating Gravitating Fluid and the Excitation by Core Motions of Decadal Fluctuations in the Earth's Rotation

General expressions (with potential applications in several areas of geophysical fluid dynamics) are derived for all three components of the contribution made by the geostrophic part of the pressure field associated with flow in a rotating gravitating fluid to the topographic torque exerted by the fluid on a rigid impermeable bounding surface of any shape. When applied to the Earth's liquid metallic core, which is bounded by nearly spherical surfaces and can be divided into two main regions, the "torosphere" and "polosphere," the expressions reduce to formulae given previously by the author, thereby providing further support for his work and that of others on the role of topographic coupling at the core-mantle boundary in the excitation by core motions of Earth rotation fluctuations on decadal time scales. They also show that recent criticisms of that work are vitiated by mathematical and physical errors. Contrary to these criticisms, the author's scheme for exploiting Earth rotation and other geophysical data (either real or simulated in computer models) in quantitative studies of the topography of the core-mantle boundary (CMB) by intercomparing various models of (a) motions in the core based on geomagnetic secular variation data and (b) CMB topography based on seismological and gravity data has a sound theoretical basis. The practical scope of the scheme is of course limited by the accuracy of real data, but this is a matter for investigation, not a priori assessment.

Hide, Raymond↗
NASA NTRS1995

Improved Bounds on Nonluminous 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 ephemeris residuals, including optical data and those two planets' Voyager 2 flybys. We extend our previous procedure by fitting more parameters of the developmental ephamerides. In addition, we present here the values for Pioneer 10, Pioneer 11, Voyager 1, and Voyager 2 Jupiter-ranging normal points (and incorporate these data as well). Our principal result is to limit DM in spherically symmetric distributions in orbit about the Sun interior to Neptune's orbit to less than Earth mass and interior to Uranus's orbit to about 1/6 of Earth's mass.

Anderson, John D.↗
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.↗