Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Differential Geometry”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 541 records · Page 30

Identification of Second Shell Coordination in Transition Metal Species Using Theoretical XANES: Example of Ti–O–(C, Si, Ge) Complexes

X-ray absorption near-edge structure (XANES) is a common technique for elucidating oxidation state and first shell coordination geometry in transition metal complexes, among many other materials. However, the structural information obtained from XANES is often limited to the first coordination sphere. In this study, we show how XANES can be used to differentiate between C, Si, and Ge in the second coordination shell of Ti–O–(C, Si, Ge) molecular complexes based on differences in their Ti K-edge XANES spectra. Experimental spectra were compared with theoretical spectra calculated using density functional theory structural optimization and ab initio XANES calculations. The unique features for second shell C, Si, and Ge present in the Ti K pre-edge XANES are attributed to the interaction between the Ti center and the O–X (X = C, Si, or Ge) antibonding orbitals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Group-invariant solutions for one dimensional, inviscid hydrodynamics

In this paper, the results of the Lie group method carried out by Ovsiannikov are utilized to study the one-dimensional hydrodynamic equations governing compressible, inviscid fluid flow in the absence of heat conduction. One-parameter subgroups of the admissible R-parameter Lie group of point transformations of the system are applied to reduce the first-order, non-linear system of partial differential equations (PDE)s to a first-order system of ordinary differential equations (ODE)s. Closed-form solutions to the reduced ODE systems are subsequently determined using a linear velocity profile ansatz. These solutions are valid in one-dimensional (1D) planar, cylindrical and spherical geometries and are connected to solutions of the governing system of PDEs through an inverse map. The linear velocity type solutions were first considered by Sedov in 1953 and constitute a subclass of all possible similarity solutions of the compressible hydrodynamics equations. They further serve as illustrative examples of using solutions obtained for the reduced ODEs to find solutions of the associated system of PDEs. Consequently, the reduced systems of ODEs are provided in their entirety inviting additional solutions to be determined via alternative explicit or numerical solution techniques.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Yield strength of CeO 2 measured from static compression in a radial diamond anvil cell

Cerium oxide (ceria, CeO 2 ) is frequently used as a standard in applications such as synchrotron and x-ray free electron lasers for calibrating x-ray wavelengths and offers the potential for understanding the high pressure properties and deformation mechanisms in a wide range of similar face centered cubic (fcc) materials. In this study, the pressure dependence of the strength of ceria was investigated up to 38 GPa using angle dispersive x-ray diffraction in a radial geometry in a diamond anvil cell. In this experiment, the difference in the stress along the axis of compression and perpendicular to the direction of compression can be determined, giving a quantity known as the differential stress. It was found that the differential stress (t), a measure of the lower bound for yield strength, initially increases rapidly from 0.35 ± 0.06 GPa to 2.2 ± 0.4 GPa at pressures of 1.8 and 3.8 GPa, respectively. Above 4 GPa, t increases more slowly to 13.8 ± 2.6 GPa at a pressure of 38 GPa. The changes in the preferred orientation (texture) of CeO 2 with pressure were also measured, allowing for the determination of active deformation mechanisms using an elasto-viscoplastic self-consistent model (EVPSC). It was found that as pressure increased, the [001] direction had a slight preferred orientation along the axis of compression. Our EVPSC model of experimental fiber (cylindrically symmetric) textures and lattice strains were most consistent with dominant slip activity along ${111}$ $\langle$$1\bar10$$\rangle$.

36 MATERIALS SCIENCE↗

Dissociation dynamics of the water dication following one-photon double ionization. I. Theory

The measurement of the triple differential cross section in the body frame for double photoionization of a molecule can be made in principle by detecting the ionic fragments and the two photoelectrons in coincidence - but only if the dynamics and geometry of dissociation of the doubly charged molecular ion are known. A classical trajectory study of the nine lowest states of the water dication is presented using high quality ab initio potential-energy surfaces. Sampling from a semiclassical initial distribution of positions and momenta is used to approximate ionization from the Frank-Condon region of the ground vibrational state of neutral H 2 O. Excellent agreement in comparison with preliminary experimental momentum imaging measurements of double photoionization of water show that eight dication states can be unambiguously identified in the experiment with the aid of theory. In conclusion, the theoretical trajectory results allow body frame measurements of double photoionization to yield all eight states even though the usual assumption of direct dissociation, the "axial recoil" approximation, breaks down for three of the dication electronic states seen in the experiment.

74 ATOMIC AND MOLECULAR PHYSICS↗

CurvilinearGrids.jl: A Julia package for curvilinear coordinate transformations

Finite-difference discretizations of partial differential equations are widespread throughout the scientific community. Oftentimes finite-differences are used to compute spatial gradients of fields on a discrete grid, which is typically a uniform or rectilinear Cartesian mesh. Arbitrary multidimensional geometry is difficult to discretize directly with finite differences, however, due to non-uniform grid spacing and non-orthogonality. Curvilinear coordinate transformations can be used as a strategy to enable arbitrary geometry. While these curvilinear transformations are straightforward, the governing PDEs require additional terms (metrics) and must adhere to strict conservation laws; these criteria complicate the application of the transformation and require careful implementation.

97 MATHEMATICS AND COMPUTING↗

Periodic motion in a class of nth-order autonomous differential equations

Sufficient conditions are obtained for the existence of periodic motion in a class of autonomous nonlinear differential equations of order greater than two. The approach is based on the decomposition of an equation into a linear and a nonlinear part. The analysis relies on some basic ideas from linear analysis and geometry. Sufficient conditions for a periodic solution are derived by means of a general topological principle referred to as the torus principle. The existence of a periodic solution is concluded by an appropriate use of the Brouwer fixed-point theorem.

Williamson, D.↗

Source of the optical red-slope in iron-rich meteorites

The relationship between ordinary chondrites and S-type asteroids is an unresolved issue in meteorite science. S-type asteroids exhibit a positively red-sloped spectrum that is interpreted to indicate the presence of elemental iron on the surfaces. The characteristic red-sloped spectrum of iron-rich meteorites is produced by only the specular component of the reflectance. Complex metallic surfaces can be modeled as linear mixtures of specular and nonspecular components. It is the geometry of the metal on a surface and its interaction with surrounding material, rather than the absolute amount of metal, that determine the redness of resulting spectra. In order to distinguish between ordinary chondrite and differentiated parent bodies it is important to understand how regolith processes affect the nature and form of metal on asteroid surfaces.

Britt, Daniel T.↗

On constructing three-dimensional overlapping grids with CMPGRD

Techniques for the construction of three-dimensional composite overlapping grids, using the grid construction program CMPGRD, are described. The overlapping approach can be used to generate grids for regions of complicated geometry. The grids can be constructed to be smooth and free from coordinate singularities. The ability to create smooth grids for complicated regions is an important first step towards the accurate numerical solution of partial differential equations. The creation of grids for surfaces defined by cross-sections such as an airplane wing is described. A method for integrating the patched surfaces generated by a computer aided design (CAD) package with the CMPGRD program is described. Additionally, the creation of grids in regions where surfaces intersect is described.

Henshaw, William D.↗

A Semi-Analytical Method for Determining the Energy Release Rate of Cracks in Adhesively-Bonded Single-Lap Composite Joints

A semi-analytical method for determining the strain energy release rate due to a prescribed interface crack in an adhesively-bonded, single-lap composite joint subjected to axial tension is presented. The field equations in terms of displacements within the joint are formulated by using first-order shear deformable, laminated plate theory together with kinematic relations and force equilibrium conditions. The stress distributions for the adherends and adhesive are determined after the appropriate boundary and loading conditions are applied and the equations for the field displacements are solved. Based on the adhesive stress distributions, the forces at the crack tip are obtained and the strain energy release rate of the crack is determined by using the virtual crack closure technique (VCCT). Additionally, the test specimen geometry from both the ASTM D3165 and D1002 test standards are utilized during the derivation of the field equations in order to correlate analytical models with future test results. The system of second-order differential field equations is solved to provide the adherend and adhesive stress response using the symbolic computation tool, Maple 9. Finite element analyses using J-integral as well as VCCT were performed to verify the developed analytical model. The finite element analyses were conducted using the commercial finite element analysis software ABAQUS. The results determined using the analytical method correlated well with the results from the finite element analyses.

Yang, Charles↗

NASA Tech Briefs, November 2010

Topics covered include: Portable Handheld Optical Window Inspection Device; Salience Assignment for Multiple-Instance Data and Its Application to Crop Yield Prediction; Speech Acquisition and Automatic Speech Recognition for Integrated Spacesuit Audio Systems ; Predicting Long-Range Traversability from Short-Range Stereo-Derived Geometry; Browser-Based Application for Telemetry Monitoring of Robotic Assets; Miniature Low-Noise G-Band I-Q Receiver; Methods of Using a Magnetic Field Response Sensor Within Closed, Electrically Conductive Containers; Differential Resonant Ring YIG Tuned Oscillator; Microfabricated Segmented-Involute-Foil Regenerator for Stirling Engines; Reducing Seal Adhesion in Low Impact Docking Systems; Optimal Flow Control Design; Corrosion-Resistant Container for Molten-Material Processing; Reusable Hot-Wire Cable Cutter; Deployment of a Curved Truss; High-Volume Airborne Fluids Handling Technologies to Fight Wildfires; Modeling of Alkane Oxidation Using Constituents and Species; Fabrication of Lanthanum Telluride 14-1-11 Zintl High-Temperature Thermoelectric Couple; A Computer Model for Analyzing Volatile Removal Assembly; Analysis of Nozzle Jet Plume Effects on Sonic Boom Signature; Optical Sidebands Multiplier; Single Spatial-Mode Room-Temperature-Operated 3.0 to 3.4 micrometer Diode Lasers; Self-Nulling Beam Combiner Using No External Phase Inverter; Portable Dew Point Mass Spectrometry System for Real-Time Gas and Moisture Analysis; Maximum Likelihood Time-of-Arrival Estimation of Optical Pulses via Photon-Counting Photodetectors; Handheld White Light Interferometer for Measuring Defect Depth in Windows; Decomposition Algorithm for Global Reachability on a Time-Varying Graph; Autonomous GN and C for Spacecraft Exploration of Comets and Asteroids; Efficient Web Services Policy Combination; Using CTX Image Features to Predict HiRISE-Equivalent Rock Density; Isolation of the Paenibacillus phoenicis, a Spore-Forming Bacterium; Monolithically Integrated, Mechanically Resilient Carbon-Based Probes for Scanning Probe Microscopy; Cell Radiation Experiment System; Process to Produce Iron Nanoparticle Lunar Dust Simulant Composite; Inversion Method for Early Detection of ARES-1 Case Breach Failure; Use of ILTV Control Laws for LaNCETS Flight Research;and Evaluating Descent and Ascent Trajectories Near Non-Spherical Bodies.

Source record↗

Quantitative measurement of binary liquid distributions using multiple-tracer x-ray fluorescence and radiography

The complex geometry and large index-of-refraction gradients that occur near the point of impingement of binary liquid jets present a challenging environment for optical interrogation. A simultaneous quadruple-tracer x-ray fluorescence and line-of-sight radiography technique is proposed as a means of distinguishing and quantifying individual liquid component distributions prior to, during, and after jet impact. Two different pairs of fluorescence tracers are seeded into each liquid stream to maximize their attenuation ratio for reabsorption correction and differentiation of the two fluids during mixing. This approach for instantaneous correction of x-ray fluorescence reabsorption is compared with a more time-intensive approach of using stereographic reconstruction of x-ray attenuation along multiple lines of sight. The proposed methodology addresses the need for a quantitative measurement technique capable of interrogating optically complex, near-field liquid distributions in many mixing systems of practical interest involving two or more liquid streams.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Geometry of matrix product states: Metric, parallel transport, and curvature

We study the geometric properties of the manifold of states described as (uniform) matrix product states. Due to the parameter redundancy in the matrix product state representation, matrix product states have the mathematical structure of a (principal) fiber bundle. The total space or bundle space corresponds to the parameter space, i.e., the space of tensors associated to every physical site. The base manifold is embedded in Hilbert space and can be given the structure of a Kähler manifold by inducing the Hilbert space metric. Our main interest is in the states living in the tangent space to the base manifold, which have recently been shown to be interesting in relation to time dependence and elementary excitations. By lifting these tangent vectors to the (tangent space) of the bundle space using a well-chosen prescription (a principal bundle connection), we can define and efficiently compute an inverse metric, and introduce differential geometric concepts such as parallel transport (related to the Levi-Civita connection) and the Riemann curvature tensor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

THE FIRST CIRCUMSTELLAR DISK IMAGED IN SILHOUETTE AT VISIBLE WAVELENGTHS WITH ADAPTIVE OPTICS: MagAO IMAGING OF ORION 218-354

We present high-resolution adaptive optics (AO) corrected images of the silhouette disk Orion 218-354 taken with Magellan AO (MagAO) and its visible light camera, VisAO, in simultaneous differential imaging mode at Hα. This is the first image of a circumstellar disk seen in silhouette with AO and is among the first visible light AO results in the literature. We derive the disk extent, geometry, intensity, and extinction profiles and find, in contrast with previous work, that the disk is likely optically thin at Hα. Our data provide an estimate of the column density in primitive, ISM-like grains as a function of radius in the disk. We estimate that only ∼10% of the total submillimeter derived disk mass lies in primitive, unprocessed grains. We use our data, Monte Carlo radiative transfer modeling, and previous results from the literature to make the first self-consistent multiwavelength model of Orion 218-354. We find that we are able to reproduce the 1-1000 μm spectral energy distribution with a ∼2-540 AU disk of the size, geometry, small versus large grain proportion, and radial mass profile indicated by our data. This inner radius is a factor of ∼15 larger than the sublimation radius of the disk, suggesting that it is likely cleared in the very interior.

79 ASTRONOMY AND ASTROPHYSICS↗

SU-E-T-432: Field Size Influence On the Electron and Photon Spectra Within Small MV Field Detectors

Purpose: To investigate the influence of photon field size on the electron and photon fluence spectra in the active volume of small field detectors. Methods: The PENELOPE MC system based usercode PenEasy was used to calculate the material influence on the spectra by scoring the differential fluence in inserts of silicon, carbon, phosphorus and aluminium having 3 mm diameter and height. The spectra were then calculated inside the active volume of eleven detectors (ion chambers and solid-state detectors) whose geometry was simulated with great detail. The inserts/detectors were placed at 10 cm depth in a 30 cm x 30 cm x 30 cm water phantom and irradiated with 2.5 MeV photons and Varian Clinac 6 MV beams of small, medium and large size. Results: For all configurations, photon spectra in the scoring volume were similar to that in a small water volume except for additional characteristic x-ray peaks resulting from the material itself and from the materials surrounding the detectors (i.e. high-Z shielding the silicon). Electron fluence calculated in the inserts were up to 60% larger than in water; the difference increased with material density and decreasing field size. MC-calculated doses were compared to analytically determined collision kerma and restricted cema (cut-off=15keV). For the inserts, with large and medium fields K-col agreed with MC-dose, but K-col overestimated the dose for small fields due to lack of lateral CPE. For the detectors, up to 15% differences between K-col and the MC-dose were found. For all configurations the C-delta and MC-dose agreed within ±2%. Conclusion: The most relevant findings were that shielding affects substantially the photon spectra and material conditions the electron spectra, their field size dependence varying with the geometry configuration. These affect the values of factors entering into relative dosimetry.

60 APPLIED LIFE SCIENCES↗

Future of Electron Scattering and Diffraction

The ability to correlate the atomic- and nanoscale-structure of condensed matter with physical properties (e.g., mechanical, electrical, catalytic, and optical) and functionality forms the core of many disciplines. Directing and controlling materials at the quantum-, atomic-, and molecular-levels creates enormous challenges and opportunities across a wide spectrum of critical technologies, including those involving the generation and use of energy. The workshop identified next generation electron scattering and diffraction instruments that are uniquely positioned to address these grand challenges. The workshop participants identified four key areas where the next generation of such instrumentation would have major impact: A – Multidimensional Visualization of Real Materials B – Atomic-scale Molecular Processes C – Photonic Control of Emergence in Quantum Materials D – Evolving Interfaces, Nucleation, and Mass Transport Real materials are comprised of complex three-dimensional arrangements of atoms and defects that directly determine their potential for energy applications. Understanding real materials requires new capabilities for three-dimensional atomic scale tomography and spectroscopy of atomic and electronic structures with unprecedented sensitivity, and with simultaneous spatial and energy resolution. Many molecules are able to selectively and efficiently convert sunlight into other forms of energy, like heat and electric current, or store it in altered chemical bonds. Understanding and controlling such process at the atomic scale require unprecedented time resolution. One of the grand challenges in condensed matter physics is to understand, and ultimately control, emergent phenomena in novel quantum materials that necessitate developing a new generation of instruments that probe the interplay among spin, charge, orbital, and lattice degrees of freedom with intrinsic time- and length-scale resolutions. Molecules and soft matter require imaging and spectroscopy with high spatial resolution without damaging their structure. The strong interaction of electrons with matter allows high-energy electron pulses to gather structural information before a sample is damaged. Electron ScatteringImaging, diffraction, and spectroscopy are the fundamental capabilities of electron-scattering instruments. The DOE BES-funded TEAM (Transmission Electron Aberration-corrected Microscope) project achieved unprecedented sub-atomic spatial resolution in imaging through aberration-corrected transmission electron microscopy. To further advance electron scattering techniques that directly enable groundbreaking science, instrumentation must advance beyond traditional two-dimensional imaging. Advances in temporal resolution, recording the full phase and energy spaces, and improved spatial resolution constitute a new frontier in electron microscopy, and will directly address the BES Grand Challenges, such as to “control the emergent properties that arise from the complex correlations of atomic and electronic constituents” and the “hidden states” “very far away from equilibrium”. Ultrafast methods, such as the pump-probe approach, enable pathways toward understanding, and ultimately controlling, the chemical dynamics of molecular systems and the evolution of complexity in mesoscale and nanoscale systems. Central to understanding how to synthesize and exploit functional materials is having the ability to apply external stimuli (such as heat, light, a reactive flux, and an electrical bias) and to observe the resulting dynamic process in situ and in operando, and under the appropriate environment (e.g., not limited to UHV conditions). To enable revolutionary advances in electron scattering and science, the participants of the workshop recommended three major new instrumental developments: A. Atomic-Resolution Multi-Dimensional Transmission Electron Microscope: This instrument would provide quantitative information over the entire real space, momentum space, and energy space for visualizing dopants, interstitials, and light elements; for imaging localized vibrational modes and the motion of charged particles and vacancies; for correlating lattice, spin, orbital, and charge; and for determining the structure and molecular chemistry of organic and soft matter. The instrument will be uniquely suited to answer fundamental questions in condensed matter physics that require understanding the physical and electronic structure at the atomic scale. Key developments include stable cryogenic capabilities that will allow access to emergent electronic phases, as well as hard/soft interfaces and radiation- sensitive materials. B. Ultrafast Electron Diffraction and Microscopy Instrument: This instrument would be capable of nano-diffraction with 10 fs temporal resolution in stroboscopic mode, and better than 100 fs temporal resolution in single shot mode. The instrument would also achieve single- shot real-space imaging with a spatial/temporal resolution of 10 nm/10 ps, representing a thousand fold improvement over current microscopes. Such a capability would be complementary to x-ray free electron lasers due to the difference in the nature of electron and x-ray scattering, enabling space-time mapping of lattice vibrations and energy transport, facilitating the understanding of molecular dynamics of chemical reactions, the photonic control of emergence in quantum materials, and the dynamics of mesoscopic materials. C. Lab-In-Gap Dynamic Microscope: This instrument would enable quantitative measurements of materials structure, composition, and bonding evolution in technologically relevant environments, including liquids, gases and plasmas, thereby assuring the understanding of structure function relationship at the atomic scale with up to nanosecond temporal resolution. This instrument would employ a versatile, modular sample stage and holder geometry to allow the multi-modal (e.g., optical, thermal, mechanical, electrical, and electrochemical) probing of materials’ functionality in situ and in operando. The electron optics encompasses a pole piece that can accommodate the new stage, differential pumping, detectors, aberration correctors, and other electron optical elements for measurement of materials dynamics. To realize the proposed instruments in a timely fashion, BES should aggressively support research and development of complementary and enabling instruments, including new electron sources, advanced electron optics, new tunable specimen pumps and sample stages, and new detectors. The proposed instruments would have transformative impact on physics, chemistry, materials science, engineering

43 PARTICLE ACCELERATORS↗

Laser speckle technique for burner liner strain measurements

Thermal and mechanical strains were measured on samples of a common material used in jet engine burner liners, which were heated from room temperature to 870 C and cooled back to 220 C, in a laboratory furnance. The physical geometry of the sample surface was recorded at selected temperatures by a set of 12 single exposure speckle-grams. Sequential pairs of specklegrams were compared in a heterodyne interferometer which give high precision measurement of differential displacements. Good speckle correlation between the first and last specklegrams is noted which allows a check on accumulate errors.

Stetson, K. A.↗

Theoretical studies of solar lasers and converters

The geometry and setup for the n-C3F7I iodine laser are illustrated. The mathematical modeling of this system is described. The chemical kinetics are summarized. A sensitivity analysis was performed on the parameters occurring in the differential equations describing the chemical kinetics.

Heinbockel, John↗

Injector Element which Maintains a Constant Mean Spray Angle and Optimum Pressure Drop During Throttling by Varying the Geometry of Tangential Inlets

A method for determining the optimum inlet geometry of a liquid rocket engine swirl injector includes obtaining a throttleable level phase value, volume flow rate, chamber pressure, liquid propellant density, inlet injector pressure, desired target spray angle and desired target optimum delta pressure value between an inlet and a chamber for a plurality of engine stages. The tangential inlet area for each throttleable stage is calculated. The correlation between the tangential inlet areas and delta pressure values is used to calculate the spring displacement and variable inlet geometry. An injector designed using the method includes a plurality of geometrically calculated tangential inlets in an injection tube; an injection tube cap with a plurality of inlet slots slidably engages the injection tube. A pressure differential across the injector element causes the cap to slide along the injection tube and variably align the inlet slots with the tangential inlets.

Trinh, Huu P.↗