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DOE OSTI2022

The Euler characteristic as a basis for teaching topology concepts to crystallographers

The simple Euler polyhedral formula, expressed as an alternating count of the bounding faces, edges and vertices of any polyhedron, V – E + F = 2, is a fundamental concept in several branches of mathematics. Obviously, it is important in geometry, but it is also well known in topology, where a similar telescoping sum is known as the Euler characteristic χ of any finite space. The value of χ can also be computed for the unit polyhedra (such as the unit cell, the asymmetric unit or Dirichlet domain) which build, in a symmetric fashion, the infinite crystal lattices in all space groups. In this application χ has a modified form (χ m ) and value because the addends have to be weighted according to their symmetry. Although derived in geometry (in fact in crystallography), χ m has an elegant topological interpretation through the concept of orbifolds. Alternatively, χ m can be illustrated using the theorems of Harriot and Descartes, which predate the discovery made by Euler. Those historical theorems, which focus on angular defects of polyhedra, are beautifully expressed in the formula of de Gua de Malves. In a still more general interpretation, the theorem of Gauss–Bonnet links the Euler characteristic with the general curvature of any closed space. This article presents an overview of these interesting aspects of mathematics with Euler's formula as the leitmotif. Finally, a game is designed, allowing readers to absorb the concept of the Euler characteristic in an entertaining way.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1978

Space solar power - An energy alternative

The space solar power concept is concerned with the use of a Space Power Satellite (SPS) which orbits the earth at geostationary altitude. Two large symmetrical solar collectors convert solar energy directly to electricity using photovoltaic cells woven into blankets. The dc electricity is directed to microwave generators incorporated in a transmitting antenna located between the solar collectors. The antenna directs the microwave beam to a receiving antenna on earth where the microwave energy is efficiently converted back to dc electricity. The SPS design promises 30-year and beyond lifetimes. The SPS is relatively pollution free as it promises earth-equivalence of 80-85% efficient ground-based thermal power plant.

Johnson, R. W.↗

NASA NTRS1997

Mechanical signals in plant development: a new method for single cell studies

Cell division, which is critical to plant development and morphology, requires the orchestration of hundreds of intracellular processes. In the end, however, cells must make critical decisions, based on a discrete set of mechanical signals such as stress, strain, and shear, to divide in such a way that they will survive the mechanical loads generated by turgor pressure and cell enlargement within the growing tissues. Here we report on a method whereby tobacco protoplasts swirled into a 1.5% agarose entrapment medium will survive and divide. The application of a controlled mechanical load to agarose blocks containing protoplasts orients the primary division plane of the embedded cells. Photoelastic analysis of the agarose entrapment medium can identify the lines of principal stress within the agarose, confirming the hypothesis that cells divide either parallel or perpendicular to the principal stress tensors. The coincidence between the orientation of the new division wall and the orientation of the principal stress tensors suggests that the perception of mechanical stress is a characteristic of individual plant cells. The ability of a cell to determine a shear-free orientation for a new partition wall may be related to the applied load through the deformation of the matrix material. In an isotropic matrix a uniaxial load will produce a rotationally symmetric strain field, which will define a shear-free plane. Where high stress intensities combine with the loading geometry to produce multiaxial loads there will be no axis of rotational symmetry and hence no shear free plane. This suggests that two mechanisms may be orienting the division plane, one a mechanism that works in rotationally symmetrical fields, yielding divisions perpendicular to the compressive tensor, parallel to the long axis of the cell, and one in asymmetric fields, yielding divisions parallel to the short axis of the cell and the compressive tensor.

NASA Discipline Number 40-50↗

NASA NTRS1994

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

Slack, David C.↗

NASA NTRS2004

Baseline Testing of Ultracapacitors for the Next Generation Launch Technology (NGLT) Project

The NASA John H. Glenn Research Center initiated baseline testing of ultracapacitors for the Next Generation Launch Transportation (NGLT) project to obtain empirical data for determining the feasibility of using ultracapacitors for the project. There are large transient loads associated with NGLT that require either a very large primary energy source or an energy storage system. The primary power source used for these tests is a proton exchange membrane (PEM) fuel cell. The energy storage system can consist of devices such as batteries, flywheels, or ultracapacitors. Ultracapacitors were used for these tests. Ultracapacitors are ideal for applications such as NGLT where long life, maintenance-free operation, and excellent low-temperature performance is essential. State-of-the-art symmetric ultracapacitors were used for these tests. The ultracapacitors were interconnected in an innovative configuration to minimize interconnection impedance. PEM fuel cells provide excellent energy density, but not good power density. Ultracapacitors provide excellent power density, but not good energy density. The combination of PEM fuel cells and ultracapacitors provides a power source with excellent energy density and power density. The life of PEM fuel cells is shortened significantly by large transient loads. Ultracapacitors used in conjunction with PEM fuel cells reduce the transient loads applied to the fuel cell, and thus appreciably improves its life. PEM fuel cells were tested with and without ultracapacitors, to determine the benefits of ultracapacitors. The report concludes that the implementation of symmetric ultracapacitors in the NGLT power system can provide significant improvements in power system performance and reliability.

Eichenberg, Dennis J.↗

NASA NTRS2005

Baseline Testing of Ultracapacitors for the Next Generation Launch Technology (NGLT) Project

Eichenberg, Dennis J.↗

NASA NTRS2002

Responses of primate caudal parabrachial nucleus and Kolliker-fuse nucleus neurons to whole body rotation

The caudal aspect of the parabrachial (PBN) and Kolliker-Fuse (KF) nuclei receive vestibular nuclear and visceral afferent information and are connected reciprocally with the spinal cord, hypothalamus, amygdala, and limbic cortex. Hence, they may be important sites of vestibulo-visceral integration, particularly for the development of affective responses to gravitoinertial challenges. Extracellular recordings were made from caudal PBN cells in three alert, adult female Macaca nemestrina through an implanted chamber. Sinusoidal and position trapezoid angular whole body rotation was delivered in yaw, roll, pitch, and vertical semicircular canal planes. Sites were confirmed histologically. Units that responded during rotation were located in lateral and medial PBN and KF caudal to the trochlear nerve at sites that were confirmed anatomically to receive superior vestibular nucleus afferents. Responses to whole-body angular rotation were modeled as a sum of three signals: angular velocity, a leaky integration of angular velocity, and vertical position. All neurons displayed angular velocity and integrated angular velocity sensitivity, but only 60% of the neurons were position-sensitive. These responses to vertical rotation could display symmetric, asymmetric, or fully rectified cosinusoidal spatial tuning about a best orientation in different cells. The spatial properties of velocity and integrated velocity and position responses were independent for all position-sensitive neurons; the angular velocity and integrated angular velocity signals showed independent spatial tuning in the position-insensitive neurons. Individual units showed one of three different orientations of their excitatory axis of velocity rotation sensitivity: vertical-plane-only responses, positive elevation responses (vertical plane plus ipsilateral yaw), and negative elevation axis responses (vertical plane plus negative yaw). The interactions between the velocity and integrated velocity components also produced variations in the temporal pattern of responses as a function of rotation direction. These findings are consistent with the hypothesis that a vestibulorecipient region of the PBN and KF integrates signals from the vestibular nuclei and relay information about changes in whole-body orientation to pathways that produce homeostatic and affective responses.

Non-NASA Center↗

NASA NTRS1982

The flux ejection dynamo effect

The mean-field effects of cyclonic convection become increasingly complex when the cyclonic rotation exceeds 1/2 pi. Net helicity is not required, with negative turbulent diffusion for instance, appearing in mirror symmetric turbulence. This paper points out a new dynamo effect arising in convective cells with strong asymmetry in the rotation of updrafts as against downdrafts. The creation of new magnetic flux arises from the ejection of reserve flux through the open boundary of the dynamo region. It is unlike the familiar alpha-effect in that individual components of the field may be amplified independently. Several formal examples are provided to illustrate the effect. Occurrence in nature depends upon the existence of fluid rotations of the order of pi in the convective updrafts. The flux ejection dynamo may possibly contribute to the generation of field in the convective core of earth and in the convective zone of the sun and other stars.

Parker, E. N.↗

DOE OSTI2023

Fundamentals of SrCoO 3-δ Based Oxygen Deficient Perovskites as Cathodes for Solid Oxide Fuel Cells

The local structure and oxygen stoichiometry in oxide systems have a profound impact on oxygen electrocatalysis encountered in metal-air batteries and solid oxide fuel cells (SOFCs). However, this knowledge is often obtained under conditions different from the real working conditions of the material, resulting in misinterpretation and misunderstanding. This PhD dissertation aims to obtain the structure and oxygen-stoichiometry information of a class of perovskite oxides under their real working conditions in solid oxide fuel cells. Several perovskite oxides were selected for the study: Sr 0.9 Y 0.1 CoO 3-δ (SYC10), Sr 0.9 Y 0.3 CoO 3-δ (SYC30), SrCo 0.9 Nb 0.1 O 3-δ (SCN10) and SrCo 0.9 Ta0.1O 3-δ (SCT10). The local crystal structure and oxygen stoichiometry of these materials were systematically characterized with in-situ neutron diffraction (ND). The oxygen stoichiometry was also measured by thermogravimetric analysis (TGA) and iodometric titration methods. To establish the correlation among structure, oxygen stoichiometry and oxygen reduction reaction (ORR) activity, high temperature electrochemical impedance spectroscopy, oxygen permeation and single cell testing were also performed. In chapter 2, SYC10 is described to have a more symmetrical structure and $V_o^{··}$ distribution, and higher $V_o^{··}$ concentration than SYC30. Molecular orbital energy analysis based on the local structure of the ORR-active Co1-polyhedra indicates SYC30 has a higher Fermi level relative to O-2p energy level in the active Co1-polyhedra, and thus a higher motional enthalpy for $V_o^{··}$ migration. However, the ORR activity of Y-doped SrCoO 3-δ (SCO) are found uncompetitive with other popular catalysts. In chapter 3 and 4, systematic structural studies are presented for Nb and Ta-doped SCO, namely SCN10 and SCT10, respectively. The methodology of unrevealing the structure-activity relationships in chapter 2 is also found applicable to SYC10, SCN10 and SCT10 as presented in chapter 5. The electrochemical tests indicate that SCT10 is the best catalyst due to its excellent thermal and electrochemical stability. In chapter 6, SCT10 is evaluated in a real solid oxide fuel cell in the form of nanoscaled SCT10 layer coating on the commercial (La 0.6 Sr 0.4 ) 0.95 Co 0.2 Fe 0.8 O 3-δ (LSCF). The bilayer structured cathode shows excellent properties of coarsening-resistant, Sr-segregation-free and high ORR-activity.

Yang, Tianrang↗

NASA NTRS2008

Modifications to Axially Symmetric Simulations Using New DSMC (2007) Algorithms

Several modifications aimed at improving physical accuracy are proposed for solving axially symmetric problems building on the DSMC (2007) algorithms introduced by Bird. Originally developed to solve nonequilibrium, rarefied flows, the DSMC method is now regularly used to solve complex problems over a wide range of Knudsen numbers. These new algorithms include features such as nearest neighbor collisions excluding the previous collision partners, separate collision and sampling cells, automatically adaptive variable time steps, a modified no-time counter procedure for collisions, and discontinuous and event-driven physical processes. Axially symmetric solutions require radial weighting for the simulated molecules since the molecules near the axis represent fewer real molecules than those farther away from the axis due to the difference in volume of the cells. In the present methodology, these radial weighting factors are continuous, linear functions that vary with the radial position of each simulated molecule. It is shown that how one defines the number of tentative collisions greatly influences the mean collision time near the axis. The method by which the grid is treated for axially symmetric problems also plays an important role near the axis, especially for scalar pressure. A new method to treat how the molecules are traced through the grid is proposed to alleviate the decrease in scalar pressure at the axis near the surface. Also, a modification to the duplication buffer is proposed to vary the duplicated molecular velocities while retaining the molecular kinetic energy and axially symmetric nature of the problem.

Liechty, Derek S.↗

DOE OSTI2021

Lower-hybrid drift waves and their interaction with plasmas in a 3D symmetric reconnection simulation with zero guide field

We investigate lower-hybrid drift waves (LHDW) in symmetric magnetic reconnection with zero guide field using three-dimensional particle-in-cell simulations. The long-wavelength mode with kρiρe∼1 develops in the bifurcated electron current layer around the X-line within the width of the electron meandering motion from the mid-plane, where ρi(e) is the ion (electron) gyroradius. The short-wavelength mode with kρe∼1 develops in the separatrix region downstream of the electron outflow jet, producing electron vortices in the background flow frame. Electrons follow the E × B drift with corrections from the diamagnetic drift and are heated inside the vortices with diverging electric fields. In the vortices, ions have comparable E × B and inertia drifts, which together mostly cancel the diamagnetic drift. Toward the center of diverging field vortices, ions are decelerated, leading to a decrease in the perpendicular temperature, while the loss of low-energy ions results in an increase in the parallel temperature. Parallel electric fields exist as a combination of the LHDW wave field projected to the magnetic field direction and the penetration of whistler waves that are mainly outside of the LHDW layer. The magnetic flux tube is twisted in the vortices. The twist may potentially lead to slippage reconnection, as indicated by the non-uniform parallel potential variation across field lines, while the periodic variations of the twisting directions are a limiting factor.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1991

Rotating bio-reactor cell culture apparatus

A bioreactor system is described in which a tubular housing contains an internal circularly disposed set of blade members and a central tubular filter all mounted for rotation about a common horizontal axis and each having independent rotational support and rotational drive mechanisms. The housing, blade members and filter preferably are driven at a constant slow speed for placing a fluid culture medium with discrete microbeads and cell cultures in a discrete spatial suspension in the housing. Replacement fluid medium is symmetrically input and fluid medium is symmetrically output from the housing where the input and the output are part of a loop providing a constant or intermittent flow of fluid medium in a closed loop.

Schwarz, Ray P.↗

NASA NTRS1992

Method for culturing mammalian cells in a perfused bioreactor

A bio-reactor system wherein a tubular housing contains an internal circularly disposed set of blade members and a central tubular filter all mounted for rotation about a common horizontal axis and each having independent rotational support and rotational drive mechanisms. The housing, blade members and filter preferably are driven at a constant slow speed for placing a fluid culture medium with discrete microbeads and cell cultures in a discrete spatial suspension in the housing. Replacement fluid medium is symmetrically input and fluid medium is symmetrically output from the housing where the input and the output are part of a loop providing a constant or intermittent flow of fluid medium in a closed loop.

Schwarz, Ray P.↗

NASA NTRS2012

Reproducing the Photospheric Magnetic Field Evolution during the Rise of Cycle 24 with Flux Transport by Supergranules

We simulate the transport of magnetic flux in the Sun s photosphere by an evolving pattern of cellular horizontal flows (supergranules). Characteristics of the simulated flow pattern can match observed characteristics including the velocity power spectrum, cell lifetimes, and cell motions in longitude and latitude. Simulations using an average, and north-south symmetric, meridional motion of the cellular pattern produce polar magnetic fields that are too weak in the North and too strong in the South. Simulations using cellular patterns with meridional motions that evolve with the observed changes in strength and north-south asymmetry will be analyzed to see if they reproduce the polar field evolution observed during the rise of Cycle 24.

Hathaway, David↗

NASA NTRS2021

Lower-Hybrid Drift Waves and Their Interaction With Plasmas in A 3D Symmetric Reconnection Simulation With Zero Guide Field

We investigate lower-hybrid drift waves (LHDW) in symmetric magnetic reconnection with zero guide field using three-dimensional particle-in-cell simulations. The long-wavelength mode with develops in the bifurcated electron current layer around the X-line within the width of the electron meandering motion from the mid-plane, where is the ion (electron) gyroradius. The short-wavelength mode with develops in the separatrix region downstream of the electron outflow jet, producing electron vortices in the background flow frame. Electrons follow the E × B drift with corrections from the diamagnetic drift and are heated inside the vortices with diverging electric fields. In the vortices, ions have comparable E × B and inertia drifts, which together mostly cancel the diamagnetic drift. Toward the center of diverging field vortices, ions are decelerated, leading to a decrease in the perpendicular temperature, while the loss of low-energy ions results in an increase in the parallel temperature. Parallel electric fields exist as a combination of the LHDW wave field projected to the magnetic field direction and the penetration of whistler waves that are mainly outside of the LHDW layer. The magnetic flux tube is twisted in the vortices. The twist may potentially lead to slippage reconnection, as indicated by the non-uniform parallel potential variation across field lines, while the periodic variations of the twisting directions are a limiting factor.

Shan Wang↗

NASA NTRS2017

Geometrically Flexible and Efficient Flow Analysis of High Speed Vehicles Via Domain Decomposition, Part 1: Unstructured-Grid Solver for High Speed Flows

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. This paper describes the key numerical methods and techniques that were found to be required to robustly obtain accurate solutions to hypersonic flows on non-hex-dominant unstructured grids. The methods and techniques described include: an augmented stencil, weighted linear least squares, cell-average gradient method, a robust multidimensional cell-average gradient-limiter process that is consistent with the augmented stencil of the cell-average gradient method and a cell-face gradient method that contains a cell skewness sensitive damping term derived using hyperbolic diffusion based concepts. A data-parallel matrix-based symmetric Gauss-Seidel point-implicit scheme, used to solve the governing equations, is described and shown to be more robust and efficient than a matrix-free alternative. In addition, a y+ adaptive turbulent wall boundary condition methodology is presented. This boundary condition methodology is deigned to automatically switch between a solve-to-the-wall and a wall-matching-function boundary condition based on the local y+ of the 1st cell center off the wall. The aforementioned methods and techniques are then applied to a series of hypersonic and supersonic turbulent flat plate unit tests to examine the efficiency, robustness and convergence behavior of the implicit scheme and to determine the ability of the solve-to-the-wall and y+ adaptive turbulent wall boundary conditions to reproduce the turbulent law-of-the-wall. Finally, the thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet flow-path is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the unstructured-grid solver for a realistic 3-D geometry on a non-hex-dominant grid.

White, Jeffery A.↗

DOE OSTI2025

Infiltrated electrodes for metal supported solid oxide electrolysis cells

Metal-supported solid oxide cells (MSOCs) are an alternative to conventional solid oxide cells (SOCs) based on ceramic cermets, offering lower material costs and higher operational flexibility. In this study symmetric MSOCs with infiltrated electrodes are explored for steam electrolysis operation to understand the underlying operation and degradation principles and suggest a direction for future MSOCs development. Two different fuel electrode backbones are used: an electronically-conductive lanthanum strontium co-doped iron nickel titanate (LSFNT) infiltrated with cerium-gadolinium oxide (CGO), or an ionic conductive zirconia based backbone (10ScYSZ) infiltrated with Ni:CGO. At the oxygen side, the backbone is 10ScYSZ, which is infiltrated with lanthanum-strontium co-doped cobalt oxide (LSC), or praseodymium oxide as cobalt-free alternative for comparison. This study suggests that the backbone electronic conductivity is key for good electrochemical performance as well as for boosting cell durability. Highly electronically conductive nanoparticles, especially nickel, were observed to irreversibly agglomerate driven by thermal conditions, whereas CGO proved to be a very stable electrocatalyst. At the fuel side, CGO (LSFNT) electrode showed lower ASR and degradation rate than Ni:CGO(ScYSZ) configuration with measured values of 0.50 Ω cm2 and 11 %/1000 h (at 0.60 A/cm2), and 0.70 Ω cm2 and 26 %/1000 h (at 0.50 A/cm2) at 1.30 V, respectively (700 °C, 50 % steam in hydrogen at the fuel side and air at the oxygen electrode side, LSC(ScYSZ) oxygen electrode).

25 ENERGY STORAGE↗

NASA NTRS2004

Computational Aerothermodynamic Simulation Issues on Unstructured Grids

The synthesis of physical models for gas chemistry and turbulence from the structured grid codes LAURA and VULCAN into the unstructured grid code FUN3D is described. A directionally Symmetric, Total Variation Diminishing (STVD) algorithm and an entropy fix (eigenvalue limiter) keyed to local cell Reynolds number are introduced to improve solution quality for hypersonic aeroheating applications. A simple grid-adaptation procedure is incorporated within the flow solver. Simulations of flow over an ellipsoid (perfect gas, inviscid), Shuttle Orbiter (viscous, chemical nonequilibrium) and comparisons to the structured grid solvers LAURA (cylinder, Shuttle Orbiter) and VULCAN (flat plate) are presented to show current capabilities. The quality of heating in 3D stagnation regions is very sensitive to algorithm options in general, high aspect ratio tetrahedral elements complicate the simulation of high Reynolds number, viscous flow as compared to locally structured meshes aligned with the flow.

Gnoffo, Peter A.↗