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Results for “Geodesic completeness”

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.

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NASA NTRS1999

Brain segmentation and the generation of cortical surfaces

This paper describes methods for white matter segmentation in brain images and the generation of cortical surfaces from the segmentations. We have developed a system that allows a user to start with a brain volume, obtained by modalities such as MRI or cryosection, and constructs a complete digital representation of the cortical surface. The methodology consists of three basic components: local parametric modeling and Bayesian segmentation; surface generation and local quadratic coordinate fitting; and surface editing. Segmentations are computed by parametrically fitting known density functions to the histogram of the image using the expectation maximization algorithm [DLR77]. The parametric fits are obtained locally rather than globally over the whole volume to overcome local variations in gray levels. To represent the boundary of the gray and white matter we use triangulated meshes generated using isosurface generation algorithms [GH95]. A complete system of local parametric quadratic charts [JWM+95] is superimposed on the triangulated graph to facilitate smoothing and geodesic curve tracking. Algorithms for surface editing include extraction of the largest closed surface. Results for several macaque brains are presented comparing automated and hand surface generation. Copyright 1999 Academic Press.

NASA Discipline Neuroscience↗
NASA NTRS2005

Strong-field Gravitational Effects in the Timing and Spectroscopy of X-Ray Binaries

Using the ray-tracing code described, we developed additional features to the hot spot model to explain the broadening of the quasi-periodic oscillation (QPO) peaks as well as the damping of higher frequency harmonics in the power spectrum. We derived a number of analytic results that agree closely with more detailed numerical calculations. Three primary pieces are developed: the superposition of multiple hot spots with finite lifetimes and random phases, a width in the radial distribution of geodesic orbits, and the scattering of photons from the hot spot through a corona around the black hole. The complete model is used to fit the observed power spectra of both type A and type B QPOs seen in XTE 51550-564, giving confidence limits on each of the model parameters. These results were presented in a conference paper and in a refereed publication. We also explored the possibility of using higher-order statistics, particularly the bispectrum and bicoherence, to distinguish between competing QPO models. These methods were applied to the hot spot model and a method was proposed to map out the spacetime metric around Kerr black holes in Ref. 3 below.

Bertschinger, Edmund↗
NASA NTRS1973

Polarization of synchrotron radiation from relativistic Schwarzschild circular geodesics.

The pattern of geodesic synchrotron radiation emitted by a charge in an orbit close to the circular photon orbit at 3M around a nonrotating black hole of mass M is studied. The analysis is carried out using Stokes parameters, which completely characterize the state of the wave. The linear polarization, as observed at infinity, is total in the orbital plane and not smaller than 90% at the half-width of the beam. At the poles, pure circular polarization would be observed. In the region between the orbit plane and the poles the polarization shows features not present in ordinary synchrotron radiation. In our model, parameters more sensitive to deviations from the orbital plane are the Stokes parameter s (sub 2) and the tilt angle of the polarization ellipse.

Breuer, R. A.↗
NASA NTRS1980

Geometric modeling and analysis of large latticed surfaces

The application of geometrical schemes, similar to geodesic domes, to large spherical antenna reflectors was investigated. The shape and size of flat segmented latticed surfaces which approximate general shells of revolution, and in particular spherical and paraboloidal reflective surfaces, were determined. The extensive mathematical and computational geometric analyses of the reflector resulted in the development of a general purpose computer program capable of generating the complete design parameters of the dish. The program also includes a graphical self contained subroutine for graphic display of the required design.

Nayfeh, A. H.↗
NASA NTRS2008

LISA Pathfinder

USA Pathfinder is a space mission dedicated to demonstrating technology for the Laser Interferometer Space Antenna (LISA). LISA is a joint ESA/NASA mission to detect low-frequency gravitational waves on the 0.0001 to 0.1 Hz frequency band. LISA is expected to observe 100's of merging massive black hole binaries out z-15, tens of thousands of close compact binary systems in the Milky Way, merging intermediate-mass black hole binaries, tens of stellar-mass black holes falling into supermassive black holes in galactic centers, and possibly other exotic sources. Several critical LISA technologies have not been demonstrated at the requisite level of performance. In spaceflight, and some fight hardware cannot be tested in a 1-g environment. Hence, the LISA Pathfinder mission is being implemented to demonstrate these critical LISA technologies in a relevant flight environment. LISA Pathfinder mimics one arm of the LISA constellation by shrinking the 5-million-kilometer armlength down to a few tens of centimeters. The experimental concept is to measure the relative separation between two test masses nominally following their own geodesics, and thereby determine the relative residual acceleration between them near 1 mHz, about a decade above the lowest frequency required by LISA. To implement such a concept, disturbances on the test masses must be kept very small by many design features, but chiefly by "drag-free" flight. A drag-free spacecraft follows a free-falling test mass which it encloses, but has no mechanical connection to. The spacecraft senses it's orientation and separation with respect to the proof mass, and its propulsion system is commanded to keep the spacecraft centered about the test mass. Thus, the spacecraft shields the test mass from most external influences, and minimizes the effect of force gradients arising from the spacecraft, and acting on the test mass. LISA Pathfinder will compare the geodesic of one test mass against that of the other. Only a metrology system based on interferometry can achieve the displacement sensitivity. Interferometers monitor the separation of both test masses with a sensitivity comparable to that required by LISA, and using the same technologies. LISA Pathfinder is scheduled to be launched in the first half of 1020 to a Lissajous orbit around the first Sun-Earth Lagrange point, L1. In addition to a complete European technology package (the LISA Technology Package, or LTP), LISA Pathfinder will also carry thrusters and software, known as ST-7, a part of NASA's New Millennium Program.

Stebbins, Robin↗