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NASA NTRS2003

A Wavelet based Suboptimal Kalman Filter for Assimilation of Stratospheric Chemical Tracer Observations

A suboptimal Kalman filter system which evolves error covariances in terms of a truncated set of wavelet coefficients has been developed for the assimilation of chemical tracer observations of CH4. This scheme projects the discretized covariance propagation equations and covariance matrix onto an orthogonal set of compactly supported wavelets. Wavelet representation is localized in both location and scale, which allows for efficient representation of the inherently anisotropic structure of the error covariances. The truncation is carried out in such a way that the resolution of the error covariance is reduced only in the zonal direction, where gradients are smaller. Assimilation experiments which last 24 days, and used different degrees of truncation were carried out. These reduced the covariance size by 90, 97 and 99 % and the computational cost of covariance propagation by 80, 93 and 96 % respectively. The difference in both error covariance and the tracer field between the truncated and full systems over this period were found to be not growing in the first case, and growing relatively slowly in the later two cases. The largest errors in the tracer fields were found to occur in regions of largest zonal gradients in the constituent field. This results indicate that propagation of error covariances for a global two-dimensional data assimilation system are currently feasible. Recommendations for further reduction in computational cost are made with the goal of extending this technique to three-dimensional global assimilation systems.

Tangborn, Andrew↗

NASA NTRS2011

Notes on Accuracy of Finite-Volume Discretization Schemes on Irregular Grids

Truncation-error analysis is a reliable tool in predicting convergence rates of discretization errors on regular smooth grids. However, it is often misleading in application to finite-volume discretization schemes on irregular (e.g., unstructured) grids. Convergence of truncation errors severely degrades on general irregular grids; a design-order convergence can be achieved only on grids with a certain degree of geometric regularity. Such degradation of truncation-error convergence does not necessarily imply a lower-order convergence of discretization errors. In these notes, irregular-grid computations demonstrate that the design-order discretization-error convergence can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all.

Diskin, Boris↗

NASA NTRS1972

Pseudorandom noise for telemetry error rate measurement applications and limitations.

A pseudorandom noise (PRN) generator functional design has been developed which is superior to the commercially available instrument in usable bandwidth and in the closeness of fit to the gaussian probability distribution in the 'tails' of the curve. The principal disadvantage of PRN sources for bit error rate (BER) measurements is that the probability distribution is truncated in the tails. This truncation of the probability distribution results in a similar truncation of the BER curve - i.e., there is a minimum BER which can be measured, below which the only possible result is zero. The minimum nonzero BER actually computed with the PRN source developed was 0.00001 with a pseudorandom sequence of 131,071 bits. It is theoretically possible, with a longer sequence, to achieve a minimum BER of 0.000001 with the same design.

Hopkins, P. M.↗

NASA NTRS1975

Dish antenna having switchable beamwidth

A switchable beamwidth antenna includes a concave parabolic main reflecting dish which has a central circular region and a surrounding coaxial annular region. A feed means selectively excites only the central region of the main dish via a truncated subreflector for wide beamwidth or substantially the entire main dish for narrow beamwidth. In one embodiment, the feed means comprises a truncated concave ellipsoid subreflector and separate feed terminations located at two foci of the ellipsoid. One feed termination directly views all of the main dish while the other feed termination, exciting the main dish via the subreflector, excites only the central region because of the subreflector truncation. In the another embodiment, the feed means comprises one feed termination and a convex hyperboloid subreflector via which the feed excites the main dish.

Schmidt, R. F.↗

NASA NTRS1980

Modal cost analysis for linear matrix-second-order systems

Reduced models and reduced controllers for systems governed by matrix-second-order differential equations are obtained by retaining those modes which make the largest contributions to quadratic control objectives. Such contributions, expressed in terms of modal data, used as mode truncation criteria, allow the statement of the specific control objectives to influence the early model reduction from very high order models which are available, for example, from finite element methods. The relative importance of damping, frequency, and eigenvector in the mode truncation decisions are made explicit for each of these control objectives: attitude control, vibration suppression and figure control. The paper also shows that using modal cost analysis (MCA) on the closed loop modes of the optimally controlled system allows the construction of reduced control policies which feedback only those closed loop modal coordinates which are most critical to the quadratic control performance criterion. In this way, the modes which should be controlled (and hence the modes which must be observable by choice of measurements), are deduced from truncations of the optimal controller.

Skelton, R. E.↗

NASA NTRS1982

Error induced by coordinate systems

It is pointed out that the choice of a curvilinear coordinate system can have a substantial effect on the error in the numerical solution of a partial differential equation. The truncation error is dependent not only on the higher order derivatives of the solution and the local grid spacing, but also on the rate-of-change of the grid spacing and on the departure of the grid from orthogonality. In connection with the present investigation, an analysis is conducted of the local truncation error in the approximation of first and second order derivatives on a curvilinear grid. Attention is given to a number of examples which illustrate the two fundamental sources of truncation error in the numerical solution of partial differential equations on curvilinear coordinate systems. The first is the grid spacing and changes in grid spacing which is measured by the first and second order derivatives of the functions defining the coordinate system. The second source is the higher order derivatives of the solution itself.

Mastin, C. W.↗

NASA NTRS1984

A modal reduction method for use with nonlinear simulations of flexible multibody spacecraft

This paper presents a modal truncation method that can be used to prepare the structural flexibility data required as input to flexible, multibody spacecraft simulation programs. The method allows one to truncate the structural models of each flexible body in the system such that the assembled system is free of undesired high frequency system modes. This truncation method enables reasonable simulation costs to be incurred while maintaining dynamic simulation fidelity in the frequency range of interest. A simple one-dimensional example is presented which provides a physical interpretation of the method's workings. In addition, results are presented from the application of the method to a complex spacecraft.

Macala, G. A.↗

NASA NTRS1985

Optimum configuration of high-lift aeromaneuvering orbital transfer vehicles in viscous flow

The results of an analysis to determine the geometrical configuration of an aeroassisted transfer vehicle with a high lift-to-drag ratio (L/D) are described and the constraints imposed on this type of entry vehicle are considered. The aerodynamic characteristics of three configurations, a flat-plate delta wing, a truncated straight cone, and a truncated bent biconic are compared. The effect of viscosity is included in the analysis which examines the rounding of the sharp leading edges. It is shown that, under the constraints of carrying a given volume in the dead air region, the values of L/D are similar for each configuration and that a small blunt leading edge only slightly affects each vehicle's aerodynamic performance, causing less than a 5 percent drop in L/D. The truncated bent biconic is found to be the only configuration that provides the necessary stabilizing moments.

Davies, C. B.↗

NASA NTRS1985

Separation of core and crustal magnetic field sources

Fluid motions in the electrically conducting core and magnetized crustal rocks are the two major sources of the magnetic field observed on or slightly above the Earth's surface. The exact separation of these two contributions is not possible without imposing a priori assumptions about the internal source distribution. Nonetheless models like these were developed for hundreds of years Gauss' method, least squares analysis with a truncated spherical harmonic expansion was the method of choice for more than 100 years although he did not address separation of core and crustal sources, but rather internal versus external ones. Using some arbitrary criterion for appropriate truncation level, we now extrapolate downward core field models through the (approximately) insulating mantle. Unfortunately our view can change dramatically depending on the degree of truncation for describing core sources.

Shure, L.↗

NASA NTRS1992

The effect of acceleration versus displacement methods on steady-state boundary forces

This study describes the acceleration and displacement methods for use in the recovery of coupled system boundary forces. A simple two degree of freedom system has been used for illustration. The effect of the choice of method for use with indeterminate or over-constrained boundaries has been investigated. It has specifically looked at results from a simple two dimensional beam problem using both methods. Much work has been done on the effect of Craig-Bampton modal truncation system displacements and forces, however, little work has been done on system level modal truncation. The findings of this study indicate that the effect of this system level truncation is significant. This may be particularly true for the 35 Hz system cutoff frequency that is required by the space shuttle. From this study's findings, recommendations for areas of study with space shuttle payload systems are made.

Mcghee, D. S.↗

NASA NTRS1991

Use of T7 RNA polymerase to direct expression of outer Surface Protein A (OspA) from the Lyme disease Spirochete, Borrelia burgdorferi

The OspA gene from a North American strain of the Lyme disease Spirochete, Borrelia burgdorferi, was cloned under the control of transciption and translation signals from bacteriophage T7. Full-length OspA protein, a 273 amino acid (31kD) lipoprotein, is expressed poorly in Escherichia coli and is associated with the insoluble membrane fraction. In contrast, a truncated form of OspA lacking the amino-terminal signal sequence which normally would direct localization of the protein to the outer membrane is expressed at very high levels (less than or equal to 100 mg/liter) and is soluble. The truncated protein was purified to homogeneity and is being tested to see if it will be useful as an immunogen in a vaccine against Lyme disease. Circular dichroism and fluorescence spectroscopy was used to characterize the secondary structure and study conformational changes in the protein. Studies underway with other surface proteins from B burgdorferi and a related spirochete, B. hermsii, which causes relapsing fever, leads us to conclude that a strategy similar to that used to express the truncated OspA can provide a facile method for producing variations of Borrelia lipoproteins which are highly expressed in E. coli and soluble without exposure to detergents.

Dunn, John J.↗

NASA NTRS1990

A New Approach to Fibrous Composite Laminate Strength Prediction

A method of predicting the strength of cross-plied fibrous composite laminates is based on expressing the classical maximum-shear-stress failure criterion for ductile metals in terms of strains. Starting with such a formulation for classical isotropic materials, the derivation is extended to orthotropic materials having a longitudinal axis of symmetry, to represent the fibers in a unidirectional composite lamina. The only modification needed to represent those same fibers with properties normalized to the lamina rather than fiber is a change in axial modulus. A mirror image is added to the strain-based lamina failure criterion for fiber-dominated failures to reflect the cutoffs due to the presence of orthogonal fibers. It is found that the combined failure envelope is now identical with the well-known maximum-strain failure model in the tension-tension and compression-compression quadrants but is truncated in the shear quadrants. The successive application of this simple failure model for fibers in the 0/90 degree and +/- 45 degree orientations, in turn, is shown to be the necessary and sufficient characterization of the fiber-dominated failures of laminates made from fibers having the same tensile and compressive strengths. When one such strength is greater than the other, the failure envelope is appropriately truncated for the lesser direct strain. The shear-failure cutoffs are now based on the higher axial strain to failure since they occur at lower strains than and are usually not affected by such mechanisms as microbuckling. Premature matrix failures can also be covered by appropriately truncating the fiber failure envelope. Matrix failures are excluded from consideration for conventional fiber/polymer composites but the additional features needed for a more rigorous analysis of exotic materials are covered. The new failure envelope is compared with published biaxial test data. The theory is developed for unnotched laminates but is easily shrunk to incorporate reductions to allow for bolt holes, cutouts, reduced compressive strength after impact, and the like.

Hart-Smith, L. J.↗

NASA NTRS1993

Vibration suppression for large scale adaptive truss structures using direct output feedback control

In this article, the vibration control of adaptive truss structures, where the control actuation is provided by length adjustable active members, is formulated as a direct output feedback control problem. A control method named Model Truncated Output Feedback (MTOF) is presented. The method allows the control feedback gain to be determined in a decoupled and truncated modal space in which only the critical vibration modes are retained. The on-board computation required by MTOF is minimal; thus, the method is favorable for the applications of vibration control of large scale structures. The truncation of the modal space inevitably introduces spillover effect during the control process. In this article, the effect is quantified in terms of active member locations, and it is shown that the optimal placement of active members, which minimizes the spillover effect (and thus, maximizes the control performance) can be sought. The problem of optimally selecting the locations of active members is also treated.

Lu, Lyan-Ywan↗

NASA NTRS1993

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.

Buchert, T.↗

NASA NTRS1994

Dynamics of binary-disk interaction. 1: Resonances and disk gap sizes

We investigate the gravitational interaction of a generally eccentric binary star system with circumbinary and circumstellar gaseous disks. The disks are assumed to be coplanar with the binary, geometrically thin, and primarily governed by gas pressure and (turbulent) viscosity but not self-gravity. Both ordinary and eccentric Lindblad resonances are primarily responsible for truncating the disks in binaries with arbitrary eccentricity and nonextreme mass ratio. Starting from a smooth disk configuration, after the gravitational field of the binary truncates the disk on the dynamical timescale, a quasi-equilibrium is achieved, in which the resonant and viscous torques balance each other and any changes in the structure of the disk (e.g., due to global viscous evolution) occur slowly, preserving the average size of the gap. We analytically compute the approximate sizes of disks (or disk gaps) as a function of binary mass ratio and eccentricity in this quasi-equilibrium. Comparing the gap sizes with results of direct simulations using the smoothed particle hydrodynamics (SPH), we obtain a good agreement. As a by-product of the computations, we verify that standard SPH codes can adequately represent the dynamics of disks with moderate viscosity, Reynolds number R approximately 10(exp 3). For typical viscous disk parameters, and with a denoting the binary semimajor axis, the inner edge location of a circumbinary disk varies from 1.8a to 2.6a with binary eccentricity increasing from 0 to 0.25. For eccentricities 0 less than e less than 0.75, the minimum separation between a component star and the circumbinary disk inner edge is greater than a. Our calculations are relevant, among others, to protobinary stars and the recently discovered T Tau pre-main-sequence binaries. We briefly examine the case of a pre-main-sequence spectroscopic binary GW Ori and conclude that circumbinary disk truncation to the size required by one proposed spectroscopic model cannot be due to Linblad resonances, even if the disk is nonviscous.

Artymowicz, Pawel↗

NASA NTRS1999

DMFS: A Data Migration File System for NetBSD

I have recently developed dmfs, a Data Migration File System, for NetBSD. This file system is based on the overlay file system, which is discussed in a separate paper, and provides kernel support for the data migration system being developed by my research group here at NASA/Ames. The file system utilizes an underlying file store to provide the file backing, and coordinates user and system access to the files. It stores its internal meta data in a flat file, which resides on a separate file system. Our data migration system provides archiving and file migration services. System utilities scan the dmfs file system for recently modified files, and archive them to two separate tape stores. Once a file has been doubly archived, files larger than a specified size will be truncated to that size, potentially freeing up large amounts of the underlying file store. Some sites will choose to retain none of the file (deleting its contents entirely from the file system) while others may choose to retain a portion, for instance a preamble describing the remainder of the file. The dmfs layer coordinates access to the file, retaining user-perceived access and modification times, file size, and restricting access to partially migrated files to the portion actually resident. When a user process attempts to read from the non-resident portion of a file, it is blocked and the dmfs layer sends a request to a system daemon to restore the file. As more of the file becomes resident, the user process is permitted to begin accessing the now-resident portions of the file. For simplicity, our data migration system divides a file into two portions, a resident portion followed by an optional non-resident portion. Also, a file is in one of three states: fully resident, fully resident and archived, and (partially) non-resident and archived. For a file which is only partially resident, any attempt to write or truncate the file, or to read a non-resident portion, will trigger a file restoration. Truncations and writes are blocked until the file is fully restored so that a restoration which only partially succeed does not leave the file in an indeterminate state with portions existing only on tape and other portions only in the disk file system. We chose layered file system technology as it permits us to focus on the data migration functionality, and permits end system administrators to choose the underlying file store technology. We chose the overlay layered file system instead of the null layer for two reasons: first to permit our layer to better preserve meta data integrity and second to prevent even root processes from accessing migrated files. This is achieved as the underlying file store becomes inaccessible once the dmfs layer is mounted. We are quite pleased with how the layered file system has turned out. Of the 45 vnode operations in NetBSD, 20 (forty-four percent) required no intervention by our file layer - they are passed directly to the underlying file store. Of the twenty five we do intercept, nine (such as vop_create()) are intercepted only to ensure meta data integrity. Most of the functionality was concentrated in five operations: vop_read, vop_write, vop_getattr, vop_setattr, and vop_fcntl. The first four are the core operations for controlling access to migrated files and preserving the user experience. vop_fcntl, a call generated for a certain class of fcntl codes, provides the command channel used by privileged user programs to communicate with the dmfs layer.

Studenmund, William↗

NASA NTRS2001

Magnetofossils in Terrestrial Samples and Martian Meteorite ALH84001

Here we compare magnetite crystals produced by terrestrial magnetotactic bacteria strain MV-1 with a subpopulation of magnetites from ALH84001. We find both to be chemically and physically identical-specifically, both are single-domain, chemically pure, and exhibit an unusual crystal habit we describe as truncated hexa-octahedral. On Earth such truncated hexa-octahedral magnetites are only known to be produced by magnetotactic bacteria. We suggest that the observation of truncated hexa-octahedral magnetites in ALH84001 are both consistent with, and in the absence of terrestrial inorganic analogs, likely formed by biogenic processes. Additional information is contained in the original extended abstract.

ThomasKeptra, Kathie L.↗

NASA NTRS2002

Wavelet Approximation in Data Assimilation

Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.

Tangborn, Andrew↗