Search NASA⌕ Search

SEARCH · Search NASA

Results for “ROOT”

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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Discrete square root filtering - A survey of current techniques.

Current techniques in square root filtering are surveyed and related by applying a duality association. Four efficient square root implementations are suggested, and compared with three common conventional implementations in terms of computational complexity and precision. It is shown that the square root computational burden should not exceed the conventional by more than 50% in most practical problems. An examination of numerical conditioning predicts that the square root approach can yield twice the effective precision of the conventional filter in ill-conditioned problems. This prediction is verified in two examples.

Kaminskii, P. G.↗
NASA NTRS1972

Discrete square root smoothing.

The basic techniques applied in the square root least squares and square root filtering solutions are applied to the smoothing problem. Both conventional and square root solutions are obtained by computing the filtered solutions, then modifying the results to include the effect of all measurements. A comparison of computation requirements indicates that the square root information smoother (SRIS) is more efficient than conventional solutions in a large class of fixed interval smoothing problems.

Kaminski, P. G.↗
NASA NTRS1976

Nonlinear Equations of Motion for Cantilever Rotor Blades in Hover with Pitch Link Flexibility, Twist, Precone, Droop, Sweep, Torque Offset, and Blade Root Offset

Nonlinear equations of motion for a cantilever rotor blade are derived for the hovering flight condition. The blade is assumed to have twist, precone, droop, sweep, torque offset and blade root offset, and the elastic axis and the axes of center of mass, tension, and aerodynamic center coincident at the quarter chord. The blade is cantilevered in bending, but has a torsional root spring to simulate pitch link flexibility. Aerodynamic forces acting on the blade are derived from strip theory based on quasi-steady two-dimensional airfoil theory. The equations are hybrid, consisting of one integro-differential equation for root torsion and three integro-partial differential equations for flatwise and chordwise bending and elastic torsion. The equations are specialized for a uniform blade and reduced to nonlinear ordinary differential equations by Galerkin's method. They are linearized for small perturbation motions about the equilibrium operating condition. Modal analysis leads to formulation of a standard eigenvalue problem where the elements of the stability matrix depend on the solution of the equilibrium equations. Two different forms of the root torsion equation are derived that yield virtually identical numerical results. This provides a reasonable check for the accuracy of the equations.

Hodges, D. H.↗
NASA NTRS1976

An algorithm for propagating the square-root covariance matrix in triangular form

A method for propagating the square root of the state error covariance matrix in lower triangular form is described. The algorithm can be combined with any triangular square-root measurement update algorithm to obtain a triangular square-root sequential estimation algorithm. The triangular square-root algorithm compares favorably with the conventional sequential estimation algorithm with regard to computation time.

Tapley, B. D.↗
NASA NTRS1981

Properties of multivariable root loci

Various properties of multivariable root loci are analyzed from a frequency domain point of view by using the technique of Newton polygons, and some generalizations of the SISO root locus rules to the multivariable case are pointed out. The behavior of the angles of arrival and departure is related to the Smith-MacMillan form of G(s) and explicit equations for these angles are obtained. After specializing to first order and a restricted class of higher order poles and zeros, some simple equations for these angles that are direct generalizations of the SISO equations are found. The unusual behavior of root loci on the real axis at branch points is studied. The SISO root locus rules for break-in and break-out points are shown to generalize directly to the multivariable case. Some methods for computing both types of points are presented.

Yagle, A. E.↗
NASA NTRS1982

Angles of multivariable root loci

A generalized eigenvalue problem is demonstrated to be useful for computing the multivariable root locus, particularly when obtaining the arrival angles to finite transmission zeros. The multivariable root loci are found for a linear, time-invariant output feedback problem. The problem is then employed to compute a closed-loop eigenstructure. The method of computing angles on the root locus is demonstrated, and the method is extended to a multivariable optimal root locus.

Thompson, P. M.↗
NASA NTRS1983

Asymptotic unbounded root loci - Formulas and computation

A new geometric way of computing the asymptotic behavior of unbounded root loci of a strictly proper linear time-invariant control system as loop gain goes to infinity is presented. Properties of certain restricted linear maps and nested restrictions of linear maps are developed, and formulas are obtained for the leading coefficient of the asymptotic values of the unbounded multivariable root loci are obtained in terms of eigenvalues of those maps. Published results and a certain simple null structure assumption are used to relate these asymptotic values to the structure at infinity of the Smith-McMillan form of the open loop transfer function. Explicit matrix formulas for the more abstract derived formulas are given and additional geometric insights are developed with orthogonal projections and singular value decomposition. Formulas for the pivots of the unbounded root loci are calculated and shown to have the same form as the coefficients of the unbounded asymptotic root loci.

Sastry, S. S.↗
NASA NTRS1984

The role of calcium in the gravitropic response of roots

Previous research has indicated that gravity-induced calcium redistribution may play an important role in the gravitropic response of shoots. Calcium was shown to move toward the upper side of gravistimulated shoots (1), and inhibitors of the calcium-activated regulator protein, calmodulin, were shown to interfere with the gravitropic response of coleoptiles (2). The potential involvement of calcium redistribution in the gravitropic response of roots by testing was examined: (1) the effect on gravitropism of calcium chelators applied to the root cap, (2) the ability of calcium gradients applied across the root cap to induce gravitropic-like curvature, and (3) the influence of gravity on the movement of Ca(45)(2+) across the root cap.

Evans, M. L.↗
NASA NTRS1982

Suppression of asymmetric acid efflux and gravitropism in maize roots treated with auxin transport inhibitors of sodium orthovanadate

In gravitropically stimulated roots of maize (Zea mays L., hybrid WF9 x 38MS), there is more acid efflux on the rapidly growing upper side than on the slowly growing lower side. In light of the Cholodny/Went hypothesis of gravitropism which states that gravitropic curvature results from lateral redistribution of auxin, the effects of auxin transport inhibitors on the development of acid efflux asymmetry and curvature in gravistimulated roots were examined. All the transport inhibitors tested prevented both gravitropism and the development of asymmetric acid efflux in gravistimulated roots. The results indicate that auxin redistribution may cause the asymmetry of acid efflux, a finding consistent with the Cholodny/Went hypothesis of gravitropism. As further evidence that auxin-induced acid efflux asymmetry may mediate gravitropic curvature, sodium orthovanadate, an inhibitor of auxin-induced H+ efflux was found to prevent both gravitropism and the development of asymmetric acid efflux in gravistimulated roots.

Mulkey, T. J.↗
NASA NTRS1985

The Interaction of Calcium and Auxin in the Gravitropic Response of Roots

The role of calcium redistribution in the responding region of the root is examined, however, the potential connection between calcium and auxin redistribution in the elongation zone is not found. The following items are examined: (1) the effect of gravity on calcium movement across the elongation zone; (2) the effect of gravity on auxin movement across the elongation zone; and (3) the effect of calcium on auxin movement across the elongation zone. It is indicated that gravistimulation induces a physiological asymmetry in the auxin transport system of maize roots and that calcium increases the total transport of auxin across the root. Gravistimulation is apparently necessary for the enhancing effect of calcium on lateral auxin movement, and it is possible that the preferential downward movement of calcium across the elongation zone of gravistimulated roots plays a role in establishing the auxin asymmetry proposed to cause positive gravitropic curvature.

Evans, M. L.↗
NASA NTRS1989

Effect of microstructure and notch root radius on fracture toughness of an aluminum metal matrix composite

Recent results on the effects of matrix aging condition (matrix temper) and notch root radius on the measured fracture toughness of a SiC particulate reinforced aluminum alloy are reviewed. Stress intensity factors at catastrophic fracture were obtained for both underaged and overaged composites reveal. The linear relation found between apparent fracture toughness and the square root of the notch root radius implies a linear dependence of the crack opening displacement on the notch root radius. The results suggest a strain controlled fracture process, and indicate that there are differences in the fracture micromechanisms of the two aging conditions.

Manoharan, M.↗
NASA NTRS1989

Effect of channel size on sweet potato storage root enlargement in the Tuskegee University hydroponic nutrient film system

The potential of the sweet potato as a food source for future long term manned space missions is being evaluated for NASA's Controlled Ecological Life Support Systems (CELSS) program. Sweet potatoes have been successfully grown in a specially designed Tuskegee University nutrient film technique (TU NFT) system. This hydroponic system yielded storage roots as high as 1790 g/plant fresh weight. In order to determine the effect of channel size on the yield of sweet potatoes, the width and depth of the growing channels were varied in two separate experiments. Widths were studied using the rectangular TU NFT channels with widths of 15 cm (6 in), 30 cm (12 in) and 45 cm (18 in). Channel depths of 5 cm (2 in), 10 cm (4 in), and 15 cm (6 in) were studied using a standard NASA fan shaped Biomass Production Chamber (BPC) channel. A comparison of preliminary results indicated that, except for storage root number, the growth and yield of sweet potatoes were not affected by channel width. Storage root yield was affected by channel depth although storage root number and foliage growth were not. Both experiments are being repeated.

Morris, Carlton E.↗
NASA NTRS1992

Aircraft ride quality controller design using new robust root clustering theory for linear uncertain systems

The aspect of controller design for improving the ride quality of aircraft in terms of damping ratio and natural frequency specifications on the short period dynamics is addressed. The controller is designed to be robust with respect to uncertainties in the real parameters of the control design model such as uncertainties in the dimensional stability derivatives, imperfections in actuator/sensor locations and possibly variations in flight conditions, etc. The design is based on a new robust root clustering theory developed by the author by extending the nominal root clustering theory of Gutman and Jury to perturbed matrices. The proposed methodology allows to get an explicit relationship between the parameters of the root clustering region and the uncertainty radius of the parameter space. The current literature available for robust stability becomes a special case of this unified theory. The bounds derived on the parameter perturbation for robust root clustering are then used in selecting the robust controller.

Yedavalli, R. K.↗
NASA NTRS1993

Robust root clustering for linear uncertain systems using generalized Lyapunov theory

Consideration is given to the problem of matrix root clustering in subregions of a complex plane for linear state space models with real parameter uncertainty. The nominal matrix root clustering theory of Gutman & Jury (1981) using the generalized Liapunov equation is extended to the perturbed matrix case, and bounds are derived on the perturbation to maintain root clustering inside a given region. The theory makes it possible to obtain an explicit relationship between the parameters of the root clustering region and the uncertainty range of the parameter space.

Yedavalli, R. K.↗
NASA NTRS1994

Root-Contact/Pressure-Plate Assembly For Hydroponic System

Hydroponic system includes growth channels equipped with rootcontact/pressure-plate assemblies. Pump and associated plumbing circulate nutrient liquid from reservoir, along bottom of growth channels, and back to reservoir. Root-contact/pressure-plate assembly in each growth channel stimulates growth of roots by applying mild contact pressure. Flat plate and plate connectors, together constitute pressure plate, free to move upward to accommodate growth of roots. System used for growing sweetpotatoes and possibly other tuber and root crops.

Morris, Carlton E.↗
NASA NTRS1993

Root gravitropism in maize and Arabidopsis

Research during the period 1 March 1992 to 30 November 1993 focused on improvements in a video digitizer system designed to automate the recording of surface extension in plants responding to gravistimulation. The improvements included modification of software to allow detailed analysis of localized extension patterns in roots of Arabidopsis. We used the system to analyze the role of the postmitotic isodiametric growth zone (a region between the meristem and the elongation zone) in the response of maize roots to auxin, calcium, touch and gravity. We also used the system to analyze short-term auxin and gravitropic responses in mutants of Arabidopsis with reduced auxin sensitivity. In a related project, we studied the relationship between growth rate and surface electrical currents in roots by examining the effects of gravity and thigmostimulation on surface potentials in maize roots.

Evans, Michael L.↗
NASA NTRS1998

The Regulation of Growth in the Distal Elongation Zone of Maize Roots

The major goals of the proposed research were 1. To develop specialized software for automated whole surface root expansion analysis and to develop technology for controlled placement of surface electrodes for analysis of relationships between root growth and root pH and electrophysiological properties. 2. To measure surface pH patterns and determine the possible role of proton flux in gravitropic sensing or response, and 3. To determine the role of auxin transport in establishment of patterns of proton flux and electrical gradients during the gravitropic response of roots with special emphasis on the role of the distal elongation zone in the early phases of the gravitropic response.

Evans, Michael L.↗
NASA NTRS2003

Root phototropism: how light and gravity interact in shaping plant form

The interactions among tropisms can be critical in determining the final growth form of plants and plant organs. We have studied tropistic responses in roots as an example of these type of interactions. While gravitropism is the predominant tropistic response in roots, phototropism also plays a role in the oriented growth in this organ in flowering plants. In blue or white light, roots exhibit negative phototropism, but red light induces positive phototropism. In the flowering plant Arabidopsis, the photosensitive pigments phytochrome A (phyA) and phytochrome B (phyB) mediate this positive red-light-based photoresponse in roots since single mutants (and the double phyAB mutant) were severely impaired in this response. While blue-light-based negative phototropism is primarily mediated by the phototropin family of photoreceptors, the phyA and phyAB mutants (but not phyB) were inhibited in this response relative to the WT. The differences observed in phototropic responses were not due to growth limitations since the growth rates among all the mutants tested were not significantly different from that of the WT. Thus, our study shows that the blue-light and red-light systems interact in plants and that phytochrome plays a key role in integrating multiple environmental stimuli.

Non-NASA Center↗