Search NASA⌕ Search

SEARCH · Search NASA

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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS2019

Streamlined Convergence Acceleration for CFD Codes

Enigma, a simplified interface to the PETSc library, is shown to enable the rapid solution of discrete partial differential equations. Two CFD codes, LAURA and HyperSolve, use Enigma to compute steady solutions of the Navier-Stokes equations. Using PETSc, Enigma is shown to provide a Jacobian-Free Newton-Krylov method (JFNK), globalized with pseudotransient continuation, that improves efficiency over the point-implicit relaxation method traditionally used by LAURA. It is shown that iterative error has a large impact on surface heat transfer predicted by LAURA on an axisymmetric sphere-cone geometry. Also, the convergence rate of HyperSolve simulating subsonic flow over a delta wing geometry with the JFNK method is shown to be more efficient than employing a defect correction method as the nonlinear solver.

Thompson, Kyle B.↗
DOE OSTI2026

High-Performance Semiempirical Excited-State Molecular Dynamics Powered by Graphics Processing Units

Here, this Letter introduces excited-state molecular dynamics in PYSEQM, a GPU-accelerated semiempirical quantum chemistry engine implemented in PyTorch. The new module enables Born–Oppenheimer molecular dynamics (BOMD) using configuration-interaction singles and random phase approximation for excited states, allowing long trajectories and large statistical ensembles to be simulated efficiently on a single GPU. We also implement an extended Lagrangian excited-state BOMD (XL-ESMD) scheme that propagates auxiliary electronic variables, enabling relaxed ground and excited-state convergence thresholds without compromising energy conservation. The excited-state BOMD implementation scales smoothly from small chromophores to a nearly 900-atom dendrimer (taking 6.5 s per MD step). PYSEQM also supports batched execution, allowing many geometries or trajectories to be evaluated in a single GPU launch, substantially increasing throughput and making ensemble-based protocols routine. As a demonstration, we compute absorption, emission, and infrared spectra from trajectories propagated on the ground and first excited states. The XL-ESMD scheme yields identical spectra at significantly lower computational cost, establishing the role of extended Lagrangian based dynamics for efficient excited-state BOMD simulations. Beyond raw performance, PYSEQM’s PyTorch foundation provides automatic differentiation for forces, efficient GPU batching, and seamless interfacing with machine learning models. These capabilities position PYSEQM as a practical platform for machine learning-augmented excited-state dynamics and lay the foundation for future data-driven nonadiabatic excited-state dynamics modeling of ultrafast spectroscopic probes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1980

Stresses in a three-dimensional unidirectional composite containing broken fibers

An approximate solution is developed for the determination of the interlaminar normal and shear stresses in the vicinity of a crack in a three dimensional composite containing unidirectional linearly elastic fibers in an infinite linearly elastic matrix. In order to reduce the complexity of the formulation, certain assumptions are made as to the physically significant stresses to be retained. These simplifications reduce the partial differential equations of elasticity to differential-difference equations which are tractable using Fourier transform techniques. This 'material modeling' approach is in contrast with solutions developed by considering each lamina as a homogeneous, orthotropic layer. The resulting solution does not contain the classical singular stress field for the fibers and the influence of broken fibers on unbroken fibers is felt by a change in stress concentration factors. The matrix stresses however, are unbounded as the fiber spacing vanishes and an equivalent fiber-matrix geometry is proposed which gives the correct singular behavior. The numerical solution is considered in detail and several specific examples are presented. The potential for damaged or debonded zones to be generated by an embedded crack is discussed, and stress concentration factors for fibers near the crack are given. Detailed comparisons are made between the present solution, the analogous two-dimensional problem, and corresponding shear-lag models.

Goree, J. G.↗
NASA NTRS1983

Preferred orbit planes in the gravitational field of a tumbling spheroidal galaxy

An analytic method is described by means of which the preferred planes into which gas will settle by dissipative differential precession in a slightly nonspherical, nonstatic potential can be determined. Attention is given to the analysis of circular orbit precession in the external potential of a slightly prolate spheroidal mass that is tumbling about a short axis, providing a crude model for barred spiral galaxies as well as for prolate elliptical ones. The results obtained agree with previous work on the existence, orientation, and stability of periodic orbits in triaxial potentials. Depending on the source and injection geometry of the gas and on the nature of dissipation in the gas, the orbital dynamics presented could lead to enhanced, or even catastrophic, radial inflow and to steady state warped structures.

Durisen, R. H.↗
DOE OSTI2025

Deciphering supramolecular and polymer-like behavior in metallogels: real-time insights into temperature-modulated gelation and rapid self-assembly dynamics

Bis(pyridyl) urea-based gelators, namely L2 and its isomeric mixture ( L1 + L2 ), are known to self-assemble into 1D architectures capable of inducing supramolecular gelation. Coordination with metal ions such as Ag( I ), Cu( II ), and Fe( III ) introduces structural reinforcement, enabling the formation of distinct 3D networks governed by metal-specific coordination geometries. Here, we present a comprehensive investigation into the temperature-responsive behavior (20–60 °C) of L2 and L1 + L2 , both in the absence and presence of Ag( I ), Dy( III ), Fe( III ), Cu( II ), and Ho( III ), using real-time small-angle neutron scattering (SANS). To probe long-term structural evolution/kinetics of self-assembly, real-time small-angle X-ray scattering (SAXS) was employed on L2 + Ag gels, complemented by differential scanning calorimetry (DSC) to evaluate thermal transitions. Our results reveal strikingly divergent gelation behaviors: L2 forms a highly rigid, covalent polymer-like network, while L1 + L2 exhibits remarkable thermal adaptability. Upon metal coordination, the assemblies exhibit pronounced crystallinity and exceptional thermal stability, as evidenced by persistent Bragg reflections and invariant d-spacings. Intriguingly, L2 : Fe (2 : 1) and L1 : L2 : Fe (0.5 : 0.5 : 1) in acetonitrile-d 3 (ACN-d 3 ) deviate from this trend, forming thermally labile amorphous gels. These systems show a complete loss of crystalline order, reduced Porod exponents—indicative of collapsed or branched fiber morphologies—and prominent melting and glass transition events in DSC. Fitting SANS and SAXS data to the correlation length model unveiled insightful nanostructural features. While most systems displayed minimal temperature-induced variation in mesh size or surface morphology, L2 : Ag in dimethyl sulfoxide-d 6 (DMSO-d 6 )/D 2 O and L2 : Fe (1 : 1) in ACN-d 3 exhibited a rare combination of thermally stable correlation lengths and increasing high- q exponents—strongly suggesting progressive fiber densification or surface smoothing within a robust gel framework. These findings highlight the tunability and structural resilience of supramolecular gels through precise control of ligand architecture, metal coordination, and temperature, offering valuable design principles for functional soft materials.

Pajoubpong, Jinnipha [Univ. of Cincinnati, OH (Uni↗
NASA NTRS1977

Ray trajectories in a torus: An application of MACSYMA to a complex numerical computation

The study of ray trajectories of plasma waves in a torodial geometry using MACSYMA is an example of how symbolic, numerical, and graphical facilities can be used in concert to accomplish a complex computational goal. Computational features of this study which are of particular significance include: the derivation of code (i.e. writing functions to generate program fragments), the use of array functions to simplify the specification of a numerical iteration scheme, and the graphical presentation of the results. Mathematically, this study originates in the solution of a linear inhomogeneous partial differential equation in 3 dimensions by the method of characteristics. While it is possible to describe this equation compactly by using vector notation, and by specifying the spatial variation of the coefficients in terms of intermediate parameters, the transformation of the equation into a form amenable to solution is very tedious. A MACSYMA program is presented for obtaining description of the rf field structure excited by a waveguide located at the edge of a toroidal plasma confinement device.

Kulp, J. L.↗
NASA NTRS1986

Tracking Landsat-5 by a differential GPS technique

As part of an international campaign to develop precise geodetic applications of the Global Positioning System (GPS), the Jet Propulsion Laboratory is conducting a demonstration of differential GPS tracking using Landsat-5. Two strategies have been investigated: one in which only the Landsat-5 orbit is estimated, and one in which both the Landsat-5 and GPS orbits are estimated together. Error studies show that under the limited conditions of the experiment, three-dimensional Landsat-5 position accuracies of about 5 m with the first strategy and 2 m with the second strategy can be achieved over a 20-min period of good observing geometry. Orbit determination results using a version of the first strategy appear to achieve the 5 m goal. This is supported by various formal error measures and independent comparisons. The more powerful strategy has yet to be carried out.

Yunck, T. P.↗
NASA NTRS1989

Study of a pursuit-evasion guidance law for high performance aircraft

The study of a one-on-one aircraft pursuit-evasion guidance scheme for high-performance aircraft is discussed. The research objective is to implement a guidance law derived earlier using differential game theory in conjunction with the theory of feedback linearization. Unlike earlier research in this area, the present formulation explicitly recognizes the two-sided nature of the pursuit-evasion scenario. The present research implements the guidance law in a realistic model of a modern high-performance fighter aircraft. Also discussed are the details of the guidance law, implementation in a highly detailed simulation of a high-performance fighter, and numerical results for two engagement geometries. Modifications of the guidance law for onboard implementation is also discussed.

Williams, Peggy S.↗
NASA NTRS1993

Helicopter approach capability using the differential global positioning system

The results of flight tests to determine the feasibility of using the Global Positioning System (GPS) in the differential mode (DGPS) to provide high accuracy, precision navigation, and guidance for helicopter approaches to landing are presented. The airborne DGPS receiver and associated equipment is installed in a NASA UH-60 Black Hawk helicopter. The ground-based DGPS reference receiver is located at a surveyed test site and is equipped with a real-time VHF data link to transmit correction information to the airborne DGPS receiver. The corrected airborne DGPS information, together with the preset approach geometry, is used to calculate guidance commands which are sent to the aircraft's approach guidance instruments. The use of DGPS derived guidance for helicopter approaches to landing is evaluated by comparing the DGPS data with the laser tracker truth data. Both standard (3 deg) and steep (6 deg and 9 deg) glideslope straight-in approaches were flown. DGPS positioning accuracy based on a time history analysis of the entire approach was 0.2 m (mean) +/- 1.8 m (2 sigma) laterally and -2.0 m (mean) +/- 3.5 m (2 sigma) vertically for 3 deg glideslope approaches, -0.1 m (mean) +/- 1.5 m (2 sigma) laterally and -1.1 m (mean) +/- 3.5 m (2 sigma) vertically for 6 deg glideslope approaches and 0.2 m (mean) +/- 1.3 m (2 sigma) laterally and -1.0 m (mean) +/- 2.8 m (2 sigma) vertically for 9 deg glideslope approaches. DGPS positioning accuracy at the 200 ft decision height (DH) on a standard 3 deg slideslope approach was 0.3 m (mean) +/- 1.5 m (2 sigma) laterally and -2.3 m (mean) +/- 1.6 m (2 sigma) vertically. These errors indicate that the helicopter position based on DGPS guidance satisfies the International Civil Aviation Organization (ICAO) Category 1 (CAT 1) lateral and vertical navigational accuracy requirements.

Kaufmann, David N.↗
NASA NTRS1993

Helicopter approach capability using the differential Global Positioning System

The results of flight tests to determine the feasibility of using the Global Positioning System (GPS) in the differential mode (DGPS) to provide high accuracy, precision navigation and guidance for helicopter approaches to landing are presented. The airborne DGPS receiver and associated equipment is installed in a NASA UH-60 Black Hawk helicopter. The ground-based DGPS reference receiver is located at a surveyed test site and is equipped with a real-time VHF data link to transmit correction information to the airborne DGPS receiver. The corrected airborne DGPS information, together with the preset approach geometry, is used to calculate guidance commands which are sent to the aircraft's approach guidance instruments. The use of DGPS derived guidance for helicopter approaches to landing is evaluated by comparing the DGPS data with the laser tracker truth data. Both standard (3 degrees) and steep (6 degrees and 9 degrees) glidescope straight-in approaches were flown. DGPS positioning accuracy based on a time history analysis of the entire approach was 0.2 m (mean) +/- 1.8 m (2 sigma) laterally and -2.0 m (mean) +/- 3.5 m (2 sigma) vertically for 3 degree glidescope approaches, -0.1 m (mean) +/- 1.5 m (2 sigma) laterally and -1.1 m (mean) +/- 3.5 m (2 sigma) vertically for 6 degree glidescope approaches, and 0.2 m (mean) +/- 1.3 m (2 sigma) laterally and -1.0 m (mean) +/- 2.8 (2 sigma) vertically for 9 degree glidescope approaches. DGPS positioning accuracy at the 200 ft decision height on a standard 3 degree glidescope approach was 0.3 m (mean) +/- 1.5 m (2 sigma) laterally and -2.3 m (mean) +/- 1.6 m (2 sigma) vertically. These errors indicate that the helicopter position based on DGPS guidance satisfies the International Civil Aviation Organization Category 1 lateral and vertical accuracy requirements.

Kaufmann, David N.↗
NASA NTRS1994

Helicopter Approach Capability Using the Differential Global Positioning System

The results of flight tests to determine the feasibility of using the Global Positioning System (GPS) in the Differential mode (DGPS) to provide high accuracy, precision navigation and guidance for helicopter approaches to landing are presented. The airborne DGPS receiver and associated equipment is installed in a NASA UH-60 Black Hawk helicopter. The ground-based DGPS reference receiver is located at a surveyed test site and is equipped with a real-time VHF data link to transmit correction information to the airborne DGPS receiver. The corrected airborne DGPS information, together with the preset approach geometry, is used to calculate guidance commands which are sent to the aircraft's approach guidance instruments. The use of DGPS derived guidance for helicopter approaches to landing is evaluated by comparing the DGPS data with the laser tracker truth data. The errors indicate that the helicopter position based on DGPS guidance satisfies the International Civil Aviation Organization (ICAO) Category 1 (CAT 1) lateral and vertical navigational accuracy requirements.

Kaufmann, David N.↗
DOE OSTI2024

Experimental Examination of Additively Manufactured Patterns on Structural Nuclear Materials for Digital Image Correlation Strain Measurements

Abstract Background There are a limited number of commercially available sensors for monitoring the deformation of materials in-situ during harsh environment applications, such as those found in the nuclear and aerospace industries. Such sensing devices, including weldable strain gauges, extensometers, and linear variable differential transformers, can be destructive to material surfaces being investigated and typically require relatively large surface areas to attach (> 10 mm in length). Digital image correlation (DIC) is a viable, non-contact alternative to in-situ strain deformation. However, it often requires implementing artificial patterns using splattering techniques, which are difficult to reproduce. Objective Additive manufacturing capabilities offer consistent patterns using programmable fabrication methods. Methods In this work, a variety of small-scale periodic patterns with different geometries were printed directly on structural nuclear materials (i.e., stainless steel and aluminum tensile specimens) using an aerosol jet printer (AJP). Unlike other additive manufacturing techniques, AJP offers the advantage of materials selection. DIC was used to track and correlate strain to alternative measurement methods during cyclic loading, and tensile tests (up to 1100 µɛ) at room temperature. Results The results confirmed AJP has better control of pattern parameters for small fields of view and facilitate the ability of DIC algorithms to adequately process patterns with periodicity. More specifically, the printed 100 μm spaced dot and 150 μm spaced line patterns provided accurate measurements with a maximum error of less than 2% and 4% on aluminum samples when compared to an extensometer and commercially available strain gauges. Conclusion Our results highlight a new pattern fabrication technique that is form factor friendly for digital image correlation in nuclear applications.

Novich, K. A. (ORCID:0000000204466022)↗
NASA NTRS1986

Near-optimal strategies for sub-decimeter satellite tracking with GPS

Decimeter tracking of low Earth orbiters using differential Global Positioning System (GPS) techniques is discussed. A precisely known global network of GPS ground receivers and a receiver aboard the user satellite are needed, and all techniques simultaneously estimate the user and GPS satellite orbits. Strategies include a purely geometric, a fully dynamic, and a hybrid strategy. The last combines dynamic GPS solutions with a geometric user solution. Two powerful extensions of the hybrid strategy show the most promise. The first uses an optimized synthesis of dynamics and geometry in the user solution, while the second uses a gravity adjustment method to exploit data from repeat ground tracks. These techniques promise to deliver subdecimeter accuracy down to the lowest satellite altitudes.

Yunck, Thomas P.↗
NASA NTRS1987

Precise near-earth navigation with GPS: A survey of techniques

The tracking accuracy of the low earth orbiters (below about 3000 km altitude) can be brought below 10 cm with a variety of differential techniques that exploit the Global Positioning System (GPS). All of these techniques require a precisely known global network of GPS ground receivers and a receiver aboard the user satellite, and all simultaneously estimate the user and GPS satellite orbits. Three basic approaches are the geometric, dynamic, and nondynamic strategies. The last combines dynamic GPS solutions with a geometric user solution. Two powerful extensions of the nondynamic strategy show considerable promise. The first uses an optimized synthesis of dynamics and geometry in the user solution, while the second uses a novel gravity-adjustment method to exploit data from repeat ground tracks. These techniques will offer sub-decimeter accuracy for dynamically unpredictable satellites down to the lowesst possible altitudes.

Yunck, T. P.↗
DOE OSTI2025

Macro-level mechanical interlocking: A rapid joining approach for additively manufactured compression molded composite panels

Composite joining typically involves multiple steps, such as drilling and surface treatment, as part of the manufacturing process, which leads to low throughput and long cycle times. In the present study, we demonstrated a macro-level mechanical interlocking (MI) based, rapid joining technique to assemble additively manufactured compression molded (AMCM) panels, enabling the production of parts larger than the mold dimensions. Composite panels made of 20 wt% short carbon fiber reinforced acrylonitrile butadiene styrene (CF/ABS) were joined using MI features of various geometries, namely tree (TR), dovetail (Dov), rectangle 2 (Rect2), and rectangle 1 (Rect1), and their in-plane strength was evaluated. The resultant strength of the tested MI joints reached up to 74 % of the baseline tensile strength (i.e., the ‘no joint’ case). Observations from optical and scanning electron microscopy revealed inadequate polymer diffusion between the adherends, indicating that the joint strength was primarily derived from mechanical interlocking. Additionally, the fracture surfaces exhibited stress-whitening marks, which were characterized using differential scanning calorimetry (DSC). The increase in melting enthalpy suggested local stretching of polymer chains due to MI. Finite element analysis (FEA) indicated that the Rect1 MI feature, which generated the lowest stress concentration, outperformed the others in terms of joint strength, achieving 42 MPa. As a demonstration of the MI joining method, a battery box tray measuring 108 cm × 34 cm using a mold with an effective dimension of 36 cm × 34 cm successfully manufactured, resulting in a part with an area three times larger than the mold. In conclusion, this study presents a promising approach to improving composite joining techniques while minimizing production complexities.

In-plane joining↗
DOE OSTI2025

From disorganized data to emergent dynamic models: Questionnaires to partial differential equations

Starting with sets of disorganized observations of spatially varying and temporally evolving systems, obtained at different (also disorganized) sets of parameters, we demonstrate the data-driven derivation of parameter dependent, evolutionary partial differential equation (PDE) models capable of generating the data. This tensor type of data is reminiscent of shuffled (multidimensional) puzzle tiles. The independent variables for the evolution equations (their “space” and “time”) as well as their effective parameters are all emergent , i.e. determined in a data-driven way from our disorganized observations of behavior in them. We use a diffusion map based questionnaire approach to build a smooth parametrization of our emergent space/time/parameter space for the data. This approach iteratively processes the data by successively observing them on the “space,” the “time” and the “parameter” axes of a tensor. Once the data become organized, we use machine learning (here, neural networks) to approximate the operators governing the evolution equations in this emergent space. Our illustrative examples are based (i) on a simple advection–diffusion model; (ii) on a previously developed vertex-plus-signaling model of Drosophila embryonic development; and (iii) on two complex dynamic network models (one neuronal and one coupled oscillator model) for which no obvious smooth embedding geometry is known a priori. This allows us to discuss features of the process like symmetry breaking, translational invariance, and autonomousness of the emergent PDE model, as well as its interpretability.

generative models↗
NASA NTRS1986

Strategies for sub-decimeter satellite tracking with GPS

Decimeter tracking of low earth orbiters can be achieved with a variety of differential GPS techniques. A precisely known global network of GPS ground receivers and a receiver aboard the user satellite are needed, and all techniques must simultaneously estimate the user and GPS satellite orbits. Three basic strategies include a purely geometric, a fully dynamic, and a hybrid strategy, the last of which combines dynamic GPS solutions with a geometric user solution. Two powerful extensions of the hybrid strategy show the most promise. The first uses a quasi-optimal synthesis of dynamics and geometry in the user solution, while the second uses a novel gravity adjustment method to exploit data from repeat ground tracks in a computationally efficient way. The best of these techniques promise to deliver sub-decimeter accuracy down to the lowest possible orbits.

Yunck, Thomas P.↗
NASA NTRS1998

Numerical Investigation of Hot Gas Ingestion by STOVL Aircraft

This report compiles the various research activities conducted under the auspices of the NASA Grant NAG3-1026, "Numerical Investigation of Hot Gas Ingestion by STOVL Aircraft" during the period of April 1989 to April 1994. The effort involved the development of multigrid based algorithms and computer programs for the calculation of the flow and temperature fields generated by Short Take-off and Vertical Landing (STOVL) aircraft, while hovering in ground proximity. Of particular importance has been the interaction of the exhaust jets with the head wind which gives rise to the hot gas ingestion process. The objective of new STOVL designs to reduce the temperature of the gases ingested into the engine. The present work describes a solution algorithm for the multi-dimensional elliptic partial-differential equations governing fluid flow and heat transfer in general curvilinear coordinates. The solution algorithm is based on the multigrid technique which obtains rapid convergence of the iterative numerical procedure for the discrete equations. Initial efforts were concerned with the solution of the Cartesian form of the equations. This algorithm was applied to a simulated STOVL configuration in rectangular coordinates. In the next phase of the work, a computer code for general curvilinear coordinates was constructed. This was applied to model STOVL geometries on curvilinear grids. The code was also validated in model problems. In all these efforts, the standard k-Epsilon model was used.

Vanka, S. P.↗