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At least 19 records

Curved Finite Elements and Curve Approximation

The approximation of parameterized curves by segments of parabolas that pass through the endpoints of each curve segment arises naturally in all quadratic isoparametric transformations. While not as popular as cubics in curve design problems, the use of parabolas allows the introduction of a geometric measure of the discrepancy between given and approximating curves. The free parameters of the parabola may be used to optimize the fit, and constraints that prevent overspill and curve degeneracy are introduced. This leads to a constrained optimization problem in two varibles that can be solved quickly and reliably by a simple method that takes advantage of the special structure of the problem. For applications in the field of computer-aided design, the given curves are often cubic polynomials, and the coefficient may be calculated in closed form in terms of polynomial coefficients by using a symbolic machine language so that families of curves can be approximated with no further integration. For general curves, numerical quadrature may be used, as in the implementation where the Romberg quadrature is applied. The coefficient functions C sub 1 (gamma) and C sub 2 (gamma) are expanded as polynomials in gamma, so that for given A(s) and B(s) the integrations need only be done once. The method was used to find optimal constrained parabolic approximation to a wide variety of given curves.

Baart, M. L.

Modelling asteroid brightness variations. II - The interpretability of light curves and phase curves

Light curves and phase curves have been computed for various asteroid models using the Lumme-Bowell (1981) scattering law. The effects of the scattering parameters on light curves were found to be almost negligible for homogeneous surfaces. The effects on phase curves were more distinct, but changing any of the scattering parameters affects the phase curves in a very similar way, making it impossible to find a unique set of parameter values corresponding to a given phase curve. Light curve amplitudes, on the other hand, depend very strongly on body shape. At least in the case of a triaxial ellipsoid it is possible to determine the axial ratios. Some observed irregularities of light curves can also be modelled easily, but the uniqueness of such models is far from obvious.

Karttunen, H.

The infrared light curve of Periodic Comet Halley 1986 III and its relationship to the visual light curve, C2, and water production rates

The near-IR light curve of Periodic Comet Halley 1986 III is analyzed and compared with C2 production, water production, and the visual light curve. This is the most complete IR light curve compiled to date for any comet. The scattering phase function at small sun-comet-earth angles is shown to affect the slope of near-IR light curve significantly. P/Halley's dust production, as inferred from the IR light curve showed an increased production rate near perihelion which appears to be correlated with the onset of significant jet activity. The near-IR light curve, visual light curve, C2, and water production rates displayed different heliocentric variations, suggesting that one parameter cannot be accurately estimated from another. This is particularly true of the early preperihelion visual light curve. A peak of 0.3-0.5 magnitude in the visual magnitude, representing the integrated brightness of the comet's visible coma, lagged the other parameters by about a day. The near-IR color, J-H, was less red during periods of strong dust activity.

Morris, Charles S.

Compression of contour data through exploiting curve-to-curve dependence

An approach to exploiting curve-to-curve dependencies in order to achieve high data compression is presented. One of the approaches to date of along curve compression through use of cubic spline approximation is taken and extended by investigating the additional compressibility achievable through curve-to-curve structure exploitation. One of the models under investigation is reported on.

Yalabik, N.

A synthetic light curve solution of the OAO-2 ultraviolet light curves of u Herculis

OAO 2 ultraviolet photometry of the eclipsing binary u Her is reported and interpreted. The light curve of u Her is found to be intrinsically variable, the variable light curve is rectified, and the adjusted light and color curves are plotted. A simultaneous solution to three adjusted OAO 2 light curves (at respective wavelengths of 3320, 1910, and 1550 A) is obtained by using the Roche model. The results indicate that the system is semidetached if the gravity darkening of the secondary is not significantly larger than expected. It is suggested that the primary is responsible for the variable light curve, that the monochromatic albedo of the secondary is very low at short wavelengths, and that the depth of primary eclipse is strongly dependent on the primary's limb darkening.

Eaton, J. A.

Preliminary Investigation of Curved Liner Sample in the NASA LaRC Curved Duct Test Rig

This viewgraph presentation reviews the preliminary investigation of the curved liner sample in the NASA LaRC Curved Duct Test Rig (CDTR). It reviews the purpose of the Curved Duct Test Rig. Its purpose is to develop capability to investigate acoustic and aerodynamic properties in ducts. It has several features to accomplish that purpose: (1) Large scale (2) Flow rate to M = 0.275 (3) Higher order mode control (4) Curved flow path (5) Adaptable test section (6) Flexible test configurations. The liner has minimal effect on turbulence or boundary layer growth in duct. The curved duct sample attenuation is affected by mode scattering. In conclusion, the CDTR is valid tool for aerodynamic and acoustic evaluation of duct treatment

Gerhold, Carl H.

Bragg Curve, Biological Bragg Curve and Biological Issues in Space Radiation Protection with Shielding

The space environment consists of a varying field of radiation particles including high-energy ions, with spacecraft shielding material providing the major protection to astronauts from harmful exposure. Unlike low-LET gamma or X-rays, the presence of shielding does not always reduce the radiation risks for energetic charged particle exposure. Since the dose delivered by the charged particle increases sharply as the particle approaches the end of its range, a position known as the Bragg peak, the Bragg curve does not necessarily represent the biological damage along the particle traversal since biological effects are influenced by the track structure of both primary and secondary particles. Therefore, the biological Bragg curve is dependent on the energy and the type of the primary particle, and may vary for different biological endpoints. To achieve a Bragg curve distribution, we exposed cells to energetic heavy ions with the beam geometry parallel to a monolayer of fibroblasts. Qualitative analyses of gamma-H2AX fluorescence, a known marker of DSBs, indicated increased clustering of DNA damage before the Bragg peak, enhanced homogenous distribution at the peak, and provided visual evidence of high linear energy transfer (LET) particle traversal of cells beyond the Bragg peak. A quantitative biological response curve generated for micronuclei (MN) induction across the Bragg curve did not reveal an increased yield of MN at the location of the Bragg peak. However, the ratio of mono-to bi-nucleated cells, which indicates inhibition in cell progression, increased at the Bragg peak location. These results, along with other biological concerns, show that space radiation protection with shielding can be a complicated issue.

Honglu, Wu

Representation of Ice Geometry by Parametric Functions: Construction of Approximating NURBS Curves and Quantification of Ice Roughness--Year 1: Approximating NURBS Curves

Software was developed to construct approximating NURBS curves for iced airfoil geometries. Users specify a tolerance that determines the extent to which the approximating curve follows the rough ice. The user can therefore smooth the ice geometry in a controlled manner, thereby enabling the generation of grids suitable for numerical aerodynamic simulations. Ultimately, this ability to smooth the ice geometry will permit studies of the effects of smoothing upon the aerodynamics of iced airfoils. The software was applied to several different types of iced airfoil data collected in the Icing Research Tunnel at NASA Glenn Research Center, and in all cases was found to efficiently generate suitable approximating NURBS curves. This method is an improvement over the current "control point formulation" of Smaggice (v.1.2). In this report, we present the relevant theory of approximating NURBS curves and discuss typical results of the software.

Dill, Loren H.

Apollo 16/AS-511/LM-11 operational calibration curves. Volume 1: Calibration curves for command service module CSM 113

Calibration curves for the Apollo 16 command service module pulse code modulation downlink and onboard display are presented. Subjects discussed are: (1) measurement calibration curve format, (2) measurement identification, (3) multi-mode calibration data summary, (4) pulse code modulation bilevel events listing, and (5) calibration curves for instrumentation downlink and meter link.

Demoss, J. F.

An analysis of the shapes of ultraviolet extinction curves. III - An atlas of ultraviolet extinction curves

The basic data needed to produce UV extinction curves for a sample of 78 stars, including spectral types, visual photometry, parameters used to produce fits to the UV extinction curves, distances to the program stars, and line-of-sight H I column densities, are presented. The observational and numerical techniques used to obtain the results are discussed in detail. The UV extinction curves and their analytic fits are shown graphically.

Fitzpatrick, Edward L.

Performance characteristics of a curved-channel microchannel plate with a curved input face and a plane output face

The presently performance-evaluated format, in which a high-gain curved-channel microchannel plate (M2MCP) has a spherical concave input face and a plane output face, allows the input face of the MCP (1) to match such curved focal surfaces as that of a Rowland-circle spectrometer mounting, while (2) having a high-resolution plane readout array in proximity focus with the output face. This MCP has been evaluated in a discrete-anode multicathode microchannel array detector system. The saturated modal gain was found to be inversely proportional to the length/diameter ratio of the channels and directly proportional to the applied MCP voltage.

Slater, David C.

Curved-Focal-Plane Arrays Using Deformed-Membrane Photodetectors

A versatile and simple approach to the design and fabrication of curved-focal-plane arrays of silicon-based photodetectors is being developed. This approach is an alternative to the one described in "Curved Focal-Plane Arrays Using Back- Illuminated High-Purity Photodetectors" (NPO-30566), NASA Tech Briefs, Vol. 27, No. 10 (October 2003), page 10a. As in the cited prior article, the basic idea is to improve the performance of an imaging instrument and simplify the optics needed to obtain a given level of performance by making an image sensor (in this case, an array of photodetectors) conform to a curved focal surface, instead of designing the optics to project an image onto a flat focal surface. There is biological precedent for curved-focal-surface designs: retinas - the image sensors in eyes - conform to the naturally curved focal surfaces of eye lenses. The present approach is applicable to both front-side- and back-side-illuminated, membrane photodetector arrays and is being demonstrated on charge-coupled devices (CCDs). The very-large scale integrated (VLSI) circuitry of such a CCD or other array is fabricated on the front side of a silicon substrate, then the CCD substrate is attached temporarily to a second substrate for mechanical support, then material is removed from the back to obtain the CCD membrane, which typically has a thickness between 10 and 20 m. In the case of a CCD designed to operate in back-surface illumination, delta doping can be performed after thinning to enhance the sensitivity. This approach is independent of the design and method of fabrication of the front-side VLSI circuitry and does not involve any processing of a curved silicon substrate. In this approach, a third substrate would be prepared by polishing one of its surfaces to a required focal-surface curvature. A CCD membrane fabricated as described above would be pressed against, deformed into conformity with, and bonded to, the curved surface. The technique used to press and bond the CCD membrane would depend on the nature of the supporting material (see figure). For example, if the third substrate were made of quartz frit, the substrate would be prepared by suffusing it with epoxy. Then one would take advantage of the porosity of the frit by applying a partial vacuum to the opposite surface of the frit, causing atmospheric pressure to push the CCD membrane against the curved surface. The curing of the epoxy would bond the CCD membrane to the curved surface. Alternatively, if the third substrate were made of a nonporous material, the curved substrate surface would be prepared by coating it with a wax or an uncured epoxy. The CCD membrane would be pressed against the coated, curved surface by use of a suitably pressurized balloon. The CCD membrane would then become bonded to the curved surface by curing of the epoxy or freezing of the wax.

Nikzad, Shouleh

Numerical investigation of an internal layer in turbulent flow over a curved hill

The development of an internal layer in a turbulent boundary layer flow over a curved hill is investigated numerically. The turbulence field of the boundary layer flow over the curved hill is compared with that of a turbulent flow over a symmetric airfoil (which has the same geometry as the curved hill except that the leading and trailing edge plates were removed) to study the influence of the strongly curved surface on the turbulence field. The turbulent flow equations are solved by a control-volume based finite difference method. The turbulence is described by a multiple-time-scale turbulence model supplemented with a near-wall turbulence model. Computational results for the mean flow field (pressure distributions on the walls, wall shearing stresses and mean velocity profiles), the turbulence structure (Reynolds stress and turbulent kinetic energy profiles), and the integral parameters (displacement and momentum thicknesses) compared favorably with the measured data. Computational results show that the internal layer is a strong turbulence field which is developed beneath the external boundary layer and is located very close to the wall. Development of the internal layer was more obviously observed in the Reynolds stress profiles and in the turbulent kinetic energy profiles than in the mean velocity profiles. In this regard, the internal layers is significantly different from wall-bounded simple shear layers in which the mean velocity profile characterizes the boundary layer most distinguishably. Development of such an internal layer, characterized by an intense turbulence field, is attributed to the enormous mean flow strain rate caused by the streamline curvature and the strong pressure gradient. In the turbulent flow over the curved hill, the internal layer begin to form near the forward corner of the hill, merges with the external boundary layer, and develops into a new fully turbulent boundary layer as the fluid flows in the downstream direction. For the flow over the symmetric airfoil, the boundary layer began to form from almost the same location as that of the curved hill, grew in its strength, and formed a fully turbulent boundary layer from mid-part of the airfoil and in the downstream region. Computational results also show that the detailed turbulence structure in the region very close to the wall of the curved hill is almost the same as that of the airfoil in most of the curved regions except near the leading edge. Thus the internal layer of the curved hill and the boundary layer of the airfoil were also almost the same. Development of the wall shearing stress and separation of the boundary layer at the rear end of the curved hill mostly depends on the internal layer and is only slightly influenced by the external boundary layer flow.

Kim, S-W.

In Vitro Experimental Model to Investigate the Biological Effects across the Bragg Curve of High-LET Radiation

The space environment consists of a varying field of radiation particles including high energy ions, with a spacecrafts shielding material providing the only major protection to astronauts from harmful exposure. Unlike lowLET gamma or Xrays, the presence of shielding does not always reduce the radiation risks for energetic charged particle exposure since the dose delivered by the charged particle increases sharply as the particle approaches the end of its range, a position known as the Bragg peak and the correlating spatial dose distribution identified as the Bragg curve. The Bragg curve does not necessarily represent the biological damage along the particle traversal since biological effects are influenced by the track structure of both primary and secondary particles. Therefore, the biological Bragg curve is dependent of the energy and the type of the primary particle, and may vary for different biological endpoints. Here we describe a unique irradiation geometry and experimental system to measure the biological response across the Bragg curve in one consistent biological sample. Polyethylene shielding was used to achieve a Bragg curve distribution with the beam geometry parallel to a monolayer of fibroblast cells. We present data that highlights the differential formation of DNA double strand breaks (DSBs) and chromosomal deletions across the Bragg curve in human fibroblasts irradiated with 600 MeV/nucleon iron ion beams. Qualitative analyses of gammaH2AX fluorescence, a known marker of DSBs, indicated potentially increased clustering of DNA damage before the Bragg peak, enhanced homogenous distribution at the peak, and provided visual evidence of high linear energy transfer (LET) particle traversal of cells beyond the Bragg peak in agreement with one-dimensional transport approximations. A biological response curve generated for micronuclei induction across the Bragg curve for 600 MeV/n Fe ions did not reveal an increase in the yield of micronuclei at the Bragg peak location. Assessment of such biological parameters employing the described in vitro experimental system may provide improved platforms to measure a number of biological consequences of shielding materials across the Bragg curve for high charge and energy (HZE) ions.

Desai, N.

Curvilinear Displacement Transfer Functions for Deformed Shape Predictions of Curved Structures Using Distributed Surface Strains

Curvilinear Displacement Transfer Functions were formulated for deformed shape predictions of different curved structures using surface strains. The embedded curved beam (depth-wise cross section of a curved structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution can be described with a piecewise linear or a piecewise nonlinear function. The discrete approach enabled piecewise integrations of a curvature-strain differential equation for the embedded curved beam to yield closed-form Curvilinear Displacement Transfer Functions, which are written in terms of embedded curved-beam geometrical parameters and surface strains. By inputting the surface strain data, the Curvilinear Displacement Transfer Functions can transform surface strains into deflections along each embedded curved beam for mapping out the overall structural deformed shapes. The finite-element method was used to analytically generate the surface strains of the curved beams. The deformed shape prediction accuracies were then determined by comparing the theoretical deflections with the finite-element-generated deflections, which were used as yardsticks. By introducing the correction factors in simple mathematical forms, the Curvilinear Displacement Transfer Functions can be quite accurate for shape predictions of different curved-beam structures ranging from limit case of straight beam up to semicircular curved beam.

Ko, William L.

On the equivalence between semiempirical fracture analyses and R-curves

The relationships between several semiempirical fracture analyses (Brockrath and Glassco, 1974; Newman, 1973; Kuhn, 1968; Orange, 1971; Feddersen, 1971) and the R-curve concept of fracture mechanics are examined. Some characteristics of the R-curve concept when applied to finite-width specimens are reviewed, and conditions for equivalence between a semiempirical analysis (SEFA) and an R-curve are derived. The relationship between R-curves and SEFAs is studied for a hypothetical material. It is shown that for each SEFA there is an equivalent R-curve, the magnitude and shape of which are determined by the SEFA formulation and parameters, and which predicts precisely the same relationship between fracture stress and original crack length. A given SEFA correlates residual strength data closely if its equivalent R-curve closely matches the actual R-curve of the material studied. The SEFA given by Newman is found to yield best results for the hypothetical case considered. Equivalent R-curves for real materials are developed using data from the literature.

Orange, T. W.