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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

The gravitational potential of a homogeneous polyhedron or don't cut corners

A polyhedron can model irregularly shaped objects such as asteroids, comet nuclei, and small planetary satellites. With minor effort, such a model can incorporate important surface features such as large craters. Here we develop closed-form expressions for the exterior gravitational potential and acceleration components due to a constant-density polyhedron. An equipotential surface of Phobos is illustrated.

Werner, Robert A.↗
NASA NTRS1993

The Earth Viewed as a Deforming Polyhedron: Method and Results

GPS is quite unlike any other geodetic technique, because we can use it to look at the Earth with high spatial and temporal resolution. For example, the GPS global network provides us with a daily snapshot of the Earth, allowing us to look with high temporal resolution at the motion of sites before, during, and after a large earthquake.The main focus of this paper is to view the Earth as an evolving polyhedron, whose vertices are defined by the GPS sites.

GPS global network GPS GPS sites deforming polyhed↗
NASA NTRS2005

Polyhedron Modeling of Rubble-Pile Asteroids

We report on progress in modeling of asteroids as collections of rigid polyhedra ("rubble piles"). Such models are (idealized) candidates for asteroid structures: aggregates of irregular rocky subunits that are held together by self-gravity and friction. We have taken several steps toward greater realism and physical interest in construction of the models (although the gravitational fields are being treated in a simplified manner). -

Korycansky, D. G.↗
NASA NTRS1980

Clipping polygon faces through a polyhedron of vision

A flight simulator combines flight data and polygon face terrain data to provide a CRT display at each window of the simulated aircraft. The data base specifies the relative position of each vertex of each polygon face therein. Only those terrain faces currently appearing within the pyramid of vision defined by the pilots eye and the edges of the pilots window need be displayed at any given time. As the orientation of the pyramid of vision changes in response to flight data, the displayed faces are correspondingly displaced, eventually moving out of the pyramid of vision. Faces which are currently not visible (outside the pyramid of vision) are clipped from the data flow. In addition, faces which are only partially outside of pyramid of vision are reconstructed to eliminate the outside portion. Window coordinates are generated defining the distance between each vertex and each of the boundary planes forming the pyramid of vision. The sign bit of each window coordinate indicates whether the vertex is on the pyramid of vision side of the associated boundary panel (positive), or on the other side thereof (negative). The set of sign bits accompanying each vertex constitute the outcode of that vertex. The outcodes (O.C.) are systematically processed and examined to determine which faces are completely inside the pyramid of vision (Case A--all signs positive), which faces are completely outside (Case C--All signs negative) and which faces must be reconstructed (Case B--both positive and negative signs).

Rohner, Michel A.↗
NASA NTRS1982

On the establishment and maintenance of a modern conventional terrestrial reference system

The frame of the Conventional Terrestrial Reference System (CTS) is defined by an adopted set of coordinates, at a fundamental epoxh, of a global network of stations which contribute the vertices of a fundamental polyhedron. A method to estimate this set of coordinates using a combination of modern three dimensional geodetic systems is presented. Once established, the function of the CTS is twofold. The first is to monitor the external (or global) motions of the polyhedron with respect to the frame of a Conventional Inertial Reference System, i.e., those motions common to all stations. The second is to monitor the internal motions (or deformations) of the polyhedron, i.e., those motions that are not common to all stations. Two possible estimators for use in earth deformation analysis are given and their statistical and physical properties are described.

Bock, Y.↗
DOE OSTI2025

Multi-plane moment-of-fluid interface reconstruction in 3D

Moment-of-fluid (MOF) methods for interface reconstruction approximate the region occupied by material in each mesh element only through reference to its geometric moments. Here, we present a 3D MOF method that represents the material (POM) in each cell as the convex intersection of the cell and multiple half-spaces, each selected to minimize the least-squares error between computed moments of the approximated material and provided reference moments. This optimization problem is highly non-linear and non-convex, making the numerical result very sensitive to the initial guess. To create an effective initial guess in each cell, we construct an ellipsoid from 0th–2nd order reference moments such that its shape corresponds with that of the POM. Within this ellipsoid we inscribe a polyhedron, and initialize the minimization problem with the half-spaces defined by each of its faces. The inscribed polyhedron has minimally 4 faces, and using up to 3rd order moments permits optimization over up to 20 unknown values. We therefore define MOF methods that utilize 4, 5, or 6 half-spaces, correspondingly initialized with the faces of a single inscribed tetrahedron, triangular prism, or hexahedron. Stability of the non-linear optimization is further improved with a prepossessing step that normalizes the reference moments according to the axes of the reference ellipsoid. Using this approach, the non-linear least-squares solver reliably converges to a near-global minimum from a single initial guess. We demonstrate accuracy and robustness using single-cell and multi-cell examples over a wide spectrum of geometry. In particular, we demonstrate our ability to exactly reproduce several important and complex features defined by up to four half-spaces, such as corners, filaments, filament tips, and embedded material in the cell.

3D interface reconstruction↗
NASA NTRS1989

Kharitonov's theorem: Generalizations and algorithms

In 1978, the Russian mathematician V. Kharitonov published a remarkably simple necessary and sufficient condition in order that a rectangular parallelpiped of polynomials be a stable set. Here, stable is taken to mean that the polynomials have no roots in the closed right-half of the complex plane. The possibility of generalizing this result was studied by numerous authors. A set, Q, of polynomials is given and a necessary and sufficient condition that the set be stable is sought. Perhaps the most general result is due to Barmish who takes for Q a polytope and proceeds to construct a complicated nonlinear function, H, of the points in Q. With the notion of stability which was adopted, Barmish asks that the boundary of the closed right-half plane be swept, that the set G is considered = to (j(omega)(bar) - infinity is less than omega is less than infinity) and for each j(omega)(sigma)G, require H(delta) is greater than 0. Barmish's scheme has the merit that it describes a true generalization of Kharitonov's theorem. On the other hand, even when Q is a polyhedron, the definition of H requires that one do an optimization over the entire set of vertices, and then a subsequent optimization over an auxiliary parameter. In the present work, only the case where Q is a polyhedron is considered and the standard definition of stability described, is used. There are straightforward generalizations of the method to the case of discrete stability or to cases where certain root positions are deemed desirable. The cases where Q is non-polyhedral are less certain as candidates for the method. Essentially, a method of geometric programming was applied to the problem of finding maximum and minimum angular displacements of points in the Nyquist locus (Q(j x omega)(bar) - infinity is less than omega is less than infinity). There is an obvious connection with the boundary sweeping requirement of Barmish.

Rublein, George↗
NASA NTRS1992

Global geodesy using GPS without fiducial sites

Baseline lengths and geocentric radii have been determined from GPS data without the use of fiducial sites. Data from the first GPS experiment for the IERS and Geodynamics (GIG '91) have been analyzed with a no-fiducial strategy. A baseline length daily repeatability of 2 mm + 4 parts per billion was obtained for baselines in the Northern Hemisphere. Comparison of baseline lengths from GPS and the global VLBI solution GLB659 (Caprette et al. 1990) show rms agreement of 2.1 parts per billion. The geocentric radius mean daily repeatability for all sites was 15 cm. Comparison of geocentric radii from GPS and SV5 (Murray et al. 1990) show rms agreement of 3.8 cm. Given n globally distributed stations, the n(n - 1)/2 baseline lengths and n geocentric radii uniquely define a rigid closed polyhedron with a well-defined center of mass. Geodetic information can be obtained by examining the structure of the polyhedron and its change with time.

Heflin, Michael↗
NASA NTRS1994

Global Geodesy Using GPS Without Fiducial Sites

Global Positioning System, GPS, used to make global geodetic measurements without use of fiducial site coordinates. Baseline lengths and geocentric radii for each site determined without having to fix any site coordinates. Given n globally distributed sites, n baseline lengths and n geocentric radii form polyhedron with each site at vertex and with geocenter at intersection of all radii. Geodetic information derived from structure of polyhedron and its change with time. Approach applied to any global geodetic technique.

Heflin, Michael B.↗
NASA NTRS2002

High Precision Grids for Neutron, Hard X-Ray, and Gamma-Ray Imaging Systems

Fourier telescopes permit observations over a very broad band of energy. They generally include synthetic spatial filtering structures, known as multilayer grids or grid pairs consisting of alternate layers of absorbing and transparent materials depending on whether neutrons or photons are being imaged. For hard x-rays and gamma rays high (absorbing) and low (transparent) atomic number elements, termed high-Z and low-Z materials may be used. Fabrication of these multilayer grid structures is not without its difficulties. Herein the alternate layers of the higher material and the lower material are inserted in a polyhedron, transparent to photons of interest, through an open face of the polyhedron. The inserted layers are then uniformly compressed to form a multilayer grid.

Jonathan W Campbell↗
DOE OSTI2025

Sharp front tracking with geometric interface reconstruction

Here, this paper presents a novel sharp front-tracking method designed to address limitations in classical front-tracking approaches, specifically their reliance on smooth interpolation kernels and extended stencils for coupling the front and fluid mesh. In contrast, the proposed method employs exclusively sharp, localized interpolation and spreading kernels, restricting the coupling to the interfacial fluid cells–those containing the interface/front. This localized coupling is achieved by integrating a divergence-preserving velocity interpolation method with a piecewise parabolic interface calculation (PPIC) and a polyhedron intersection algorithm to compute the indicator function and local interface curvature. Surface tension is computed using the Continuum Surface Force (CSF) method, maintaining consistency with the sharp representation. Additionally, we propose an efficient local roughness smoothing implementation to account for surface mesh undulations, which is easily applicable to any triangulated surface mesh. Building on our previous work, the primary innovation of this study lies in the localization of the coupling for both the indicator function and surface tension calculations. By reducing the interface thickness on the fluid mesh to a single cell, as opposed to the 4–5 cell spans typical in classical methods, the proposed sharp front-tracking method achieves a highly localized and accurate representation of the interface. This sharper representation mitigates parasitic currents and improves force balancing, making it particularly suitable for scenarios where the interface plays a critical role, such as microfluidics, fluid-fluid interactions, and fluid-structure interactions. The proposed method is comprehensively validated and tested on canonical interfacial flow problems, including stationary and translating Laplace equilibria, oscillating droplets, and rising bubbles. The presented results demonstrate that the sharp front-tracking method significantly outperforms the classical approach in terms of accuracy, stability, and computational efficiency. Notably, parasitic currents are reduced by approximately two orders of magnitude and stable results are obtained for parameter ranges where classical front tracking fails to converge.

42 ENGINEERING↗
DOE OSTI2025

Organic Modulators Enable Morphological Diversity in Colloidal Crystals Engineered with DNA

Colloidal crystal engineering with DNA is a powerful way of generating a wide variety of crystals spanning over 90 different symmetries. However, in many cases, crystals with well-defined habits are difficult, if not impossible, to make, in part due to rapid crystal defect formation and propagation. This is especially true in the case of face-centered cubic (FCC) structures. Herein, we report a strategy that uses formamide as a chemical modulator to slow down colloidal crystal growth, which decreases defect formation and yields higher-quality crystals. Formamide forms hydrogen bonds with DNA bases and destabilizes the DNA duplex; in the context of colloidal crystallization, formamide leads to the disassembly of undercoordinated particles (defect architectures) and facilitates their reassembly into structures with the maximum number of nearest-neighbor contacts and DNA bonds. Here, when targeting an FCC lattice comprised of DNA-modified spherical 20 nm particles, formamide promotes the formation of its Wulff polyhedron (a truncated octahedron), never observed before in colloidal crystal engineering with DNA. Importantly, kinetic habits, including tetrahedra, octahedra, icosahedra, and decahedra, are also observed depending on formamide concentration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Towards libraries of different ultrasmall amorphous silica cage topologies

Cage topology controlled at the nanometer length scale is expected to enable original functionalities, e.g., in catalysis and therapeutics. Cages are fundamental structural motifs of clathrates and their topological duals, Frank-Kasper phases, and are constituents of mesoporous silica frameworks. However, with one exception, they have not been synthesized as discrete particles. By varying reactant ratios of surfactant, oil, and silane, we report the discovery of 5(12)6(2) and 5(12)6(8) amorphous silica polyhedra, each coexisting with the previously identified 5(12) cage, using combined cryo-transmission electron microscopy (cryo-TEM) and single-particle reconstruction (SPR). Notably, the 5(12)6(8) polyhedron represents a topology not previously observed in mesoporous silica frameworks. Control over structural features is demonstrated, and insights into cage formation mechanisms are provided. Structural outcomes are summarized in a ternary morphology diagram alongside prior results, bridging serendipitous discovery and intentional design of silica cages displaying a level of control over silica polymerization rivaling nature.

Jang, Dong June [Department of Materials Science a↗