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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
DOE OSTI2023

First Moments of a Polyhedron Clipped by a Paraboloid

We provide closed-form expressions for the first moments (i.e., the volume and volume-weighted centroid) of a polyhedron clipped by a paraboloid, that is, of a polyhedron intersected with the subset of the three-dimensional real space located on one side of a paraboloid. These closed-form expressions are derived following successive applications of the divergence theorem and the judicious parametrization of the intersection of the polyhedron’s faces with the paraboloid. Here, we provide means for identifying ambiguous discrete intersection topologies, and propose a corrective procedure for preventing their occurence. Finally, we put our proposed closed-form expressions and numerical approach to the test with millions of random and manually engineered polyhedron/paraboloid intersection configurations. The results of these tests show that we are able to provide robust machine-accurate estimates of the first moments at a computational cost that is within one order of magnitude of that of state-of-the-art half-space clipping algorithms.

97 MATHEMATICS AND COMPUTING↗
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↗
DOE OSTI2022

Synthesis of perovskite polyhedron nanocrystals with equivalent facets and the controlled growth of Pt nanoparticles with differing surface concentration of oxidized Pt 4+ /Pt 2+ species

Co-existence of different surfaces in traditional polycrystalline heterogeneous catalysts imposes a challenge to induce different kinds of catalytic species and average reactivity. Supported metal/oxide model catalyst designed with equivalent well-defined surfaces and active species provides an opportunity to control the uniformity, maintain efficient activity, and understand catalytic mechanisms at the atomic and molecular levels. Herein, sub-20 nm perovskite-structure BaTiO 3 polyhedron nanocuboids and Zr-substituted rhombic dodecahedron nanocrystals were synthesized and employed as the oxide support for the subsequent uniform growth of 1–2 nm Pt nanoparticles. These Pt nanoparticles were well dispersed on the 12 equivalent (110) facets of BaTi 0.75 Zr 0.25 O 3 rhombic dodecahedra and on the 6 equivalent (100) facets of BaTiO 3 nanocuboids. The main active centers on the Pt/BaTi 0.75 Zr 0.25 O 3 catalysts in the oxidized surface layer of Pt (111) facets are Pt 4+ versus Pt 2+ , which is in contrast to the oxidized surface layer of the Pt (100) facets on the Pt/BaTiO 3 cuboids where there are a greater number of Pt 2+ species. Compared with Pt/BaTiO 3 nanocuboids, the Pt/BaTi 0.75 Zr 0.25 O 3 catalysts demonstrated higher CO catalytic oxidation activity with a lower apparent Arrhenius activation energy. Finally, this work advances our ability to synthesize metal/oxide model catalyst that offer equivalent facets and highly uniform active centers with reasonable surface area in order to gain insight in reaction mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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.↗
DOE OSTI2022

Pauling’s rules for oxide-based minerals: A re-examination based on quantum mechanical constraints and modern applications of bond-valence theory to Earth materials

Since their introduction in 1929, Pauling’s five rules have been used by scientists from many disciplines to rationalize and predict stable arrangements of atoms and coordination polyhedra in crystalline solids; amorphous materials such as silicate glasses and melts; nanomaterials, poorly crystalline solids; aqueous cation and anion complexes; and sorption complexes at mineral-aqueous solution interfaces. The predictive power of these simple yet powerful rules was challenged recently by George et al. (2020), who performed a statistical analysis of the performance of Pauling’s five rules for about 5000 oxide crystal structures. They concluded that only 13% of the oxides satisfy the last four rules simultaneously and that the second rule has the most exceptions. They also found that Pauling’s first rule is satisfied for only 66% of the coordination environments tested and concluded that no simple rule linking ionic radius to coordination environment will be predictive due to the variable quality of univalent radii. We address these concerns and discuss quantum mechanical calculations that complement Pauling’s rules, particularly his first (radius sum and radius ratio rule) and second (electrostatic valence rule) rules. We also present a more realistic view of the bonded radii of atoms, derived by determining the local minimum in the electron density distribution measured along trajectories between bonded atoms known as bond paths, i.e., the bond critical point (rc). Electron density at the bond critical point is a quantum mechanical observable that correlates well with Pauling bond strength. Moreover, a metal atom in a polyhedron has as many bonded radii as it has bonded interactions, resulting in metal and O atoms that may not be spherical. O atoms, for example, are not spherical in many oxide-based crystal structures. Instead, the electron density of a bonded oxygen is often highly distorted or polarized, with its bonded radius decreasing systematically from ~1.38 Å when bonded to highly electropositive atoms like sodium to 0.64 Å when bonded to highly electronegative atoms like nitrogen. Bonded radii determined for metal atoms match the Shannon (1976) radii for more electropositive atoms, but the match decreases systematically as the electronegativities of the M atoms increase. As a result, significant departures from the radius ratio rule in the analysis by George et al. (2020) is not surprising. We offer a modified, more fundamental version of Pauling’s first rule and demonstrate that the second rule has a one-to-one connection between the electron density accumulated between the bonded atoms at the bond critical point and the Pauling bond strength of the bonded interaction. Pauling’s second rule implicitly assumes that bond strength is invariant with bond length for a given pair of bonded atoms. Many studies have since shown that this is not the case, and Brown and Shannon (1973) developed an equation and a set of parameters to describe the relation between bond length and bond strength, now redefined as bond valence to avoid confusion with Pauling bond-strength. Brown (1980) used the valence-sum rule, together with the path rule and the valence-matching principle, as the three axioms of bond-valence theory (BVT), a powerful method for understanding many otherwise elusive aspects of crystals and also their participation in dynamic processes. We show how a priori bond-valence calculations can predict unstrained bond-lengths and how bond-valence mapping can locate low-Z atoms in a crystal structure (e.g., Li) or examine possible diffusion pathways for atoms through crystal structures. In addition, we briefly discuss Pauling’s third, fourth, and fifth rules, the first two of which concern the sharing of polyhedron elements (edges and faces) and the common instability associated with structures in which a polyhedron shares an edge or face with another polyhedron and contains high-valence cations. The olivine [α-(MgxFe1–x)2SiO4] crystal structure is used to illustrate the distortions from hexagonal close-packing of O atoms caused by metal-metal repulsion across shared polyhedron edges. We conclude by discussing several applications of BVT to Earth materials, including the use of BVT to: (1) locate H+ ions in crystal structures, including the location of protons in the crystal structures of nominally anhydrous minerals in Earth’s mantle; (2) determine how strongly bonded (usually anionic) structural units interact with weakly bonded (usually cationic) interstitial complexes in complex uranyl-oxide and uranyl-oxysalt minerals using the valence-matching principle; (3) calculate Lewis acid strengths of cations and Lewis base strengths of anions; (4) determine how (H2O) groups can function as bond-valence transformers by dividing one bond into two bonds of half the bond valence; (5) help characterize products of sorption reactions of aqueous cations (e.g., Co2+ and Pb2+) and oxyanions [e.g., selenate (Se6+O4)2- and selenite (Se4+O3)2-] at mineral-aqueous solution interfaces and the important role of protons in these reactions; and (6) help characterize the local coordination environments of highly charged cations (e.g., Zr4+, Ti4+, U4+, U5+, and U6+) in silicate glasses and melts.

Geochemistry & Geophysics↗
DOE OSTI2020

An ab initio molecular dynamics exploration of associates in Ba-Bi liquid with strong ordering trends

Fictive associates are widely used to describe and model liquid phases with strong ordering trends. However, little evidence is known about the assumed associates in most cases. In the present work, an ab initio molecular dynamics (AIMD) study is employed to investigate the characters of the Ba-Bi liquid, in which associates have been assumed in existing thermodynamic modeling. It is found that in the Ba rich melt, the Bi atoms are almost completely surrounded by Ba atoms. The Bi-centered coordination polyhedrons are strongly associated to crystalline structures of Ba 5 Bi 3 and Ba 4 Bi 3 with a longer lifetime than other polyhedrons during the AIMD simulations. In addition, these Bi-centered polyhedrons in Ba rich melt connect with each other through vertex, edge, face, and/or bipyramid sharing to form medium range orders (MRO). In the Bi rich melt, the Ba-centered polyhedrons also form MROs, but they are both structurally and compositionally diverse with a shorter lifetime. These findings from AIMD study provide evidences that there exist a strongly ordering Ba 4 Bi 3 associate and a weakly ordering BaBi 3 associate in the Ba-Bi liquid. Here, the predicted enthalpy of mixing in the liquid agrees well with the results by the CALPHAD modeling in the literature.

36 MATERIALS SCIENCE↗
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↗
DOE OSTI2021

Bulk Diffusion of Cl through O Vacancies in α-Cr 2 O 3 : A Density Functional Theory Study

Many metals form passive oxides which are broken or weakened by anionic-induced degradation leading to material failure and anionic diffusion is an important step of this degradation process. The diffusion of anionic species through oxides involves a combination of diffusion along grain boundaries, cracks, and channels, as well as bulk diffusion via point defects which is the focus of this study. Using density functional theory, we study bulk diffusion of Cl through O vacancies in α -Cr 2 O 3 as a model system for passive metal oxides. Little is known about Cl diffusion and bonding characteristics, so we benchmark our work through comparison to numerous studies on O diffusion in α -Cr 2 O 3 to analyze similarities and differences between the O and Cl diffusion in the passivation and degradation process of α -Cr 2 O 3 respectively. Unlike O diffusion, the lowest diffusion barrier for Cl is cross-plane diffusion between two (0001) planes through a vacant cation site but the much shorter in-plane diffusion path within the same coordination polyhedron has 35% higher barrier. This work provides the basis for considering the contributions of Cl bulk-diffusion in the overall diffusion kinetics of Cl through α -Cr 2 O 3 .

Oware Sarfo, Kofi↗
DOE OSTI2021

Gravitation and Mesh Adaption

The Gravitation and Mesh Adaptation (GaMA) toolbox consists of a set of Matlab classes for modeling the environment around asteroids and comets. A variety of gravitational models and supporting algorithms from are consolidated alongside a custom meshing utility tailored for the application. This allows the user to work within a single streamlined environment to import and manipulate surface definitions, probe the dynamical environment, integrate trajectories, and post-process results. For other applications, modified surface meshes can be exported. Gravity Models: 1) Werner's analytic polyhedron model 2) Mascon model 3) Gottlieb's spherical harmonic model 4) Approximate polyhedron models 5) Curvilinear surface models 6) Custom composite models Meshing Features: 1) Array-based half-edge data structure 2) Supports curvilinear surface definitions up to degree 4 3) Ray-tracing 4) Coarsening 5) Feature-based refinement 6) Projection 7) Smoothing 8) Mesh quality validity tests 9) Mesh repair Additional Features: 1) Solar radiation pressure model 2) Distant 3rd body model 3) Collision detection 4) Trajectory integration and post-processing 5) Visualization of surface fields

Pearl, Jason↗
DOE OSTI2022

Cutting Corners: Curvilinear-Surface-Based Gravity Models for Asteroids and Comets

We report that asteroids and comets are often highly irregular in shape and can contain large density inhomogenities. For such bodies, the simple point-mass gravity model does not capture the dynamics of the environment and this has driven a need for higher fidelity alternatives. A number of approaches have been developed with one of the most popular being the analytic polyhedral model. The analytic polyhedral model approximates the irregular shaped body as a polyhedron, typically consisting of triangular facets, with some assumed internal density distribution. Several analytic formulations have been derived for the gravitational fields of a constant-density polyhedron. A thorough history of the model is provided in Ref. [6] as well as a comparison of the implementations of Refs. [2–4]. The three versions provide near identical accuracy with the implementation of Werner requiring the fewest transcendental function evaluations suggesting its superior efficiency. Implementations with linear density contrasts and arbitrary polynomial density contrasts have also been developed.

79 ASTRONOMY AND ASTROPHYSICS↗
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↗