Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “space and time decomposition”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Imposing equilibrium on experimental 3-D stress fields using Hodge decomposition and FFT-based optimization

Here, we present a methodology to impose micromechanical constraints, i.e. stress equilibrium at grain and sub-grain scale, to an arbitrary (non-equilibrated) voxelized stress field obtained, for example, by means of synchrotron X-ray diffraction techniques. The method consists in finding the equilibrated stress field closest (in L 2 -norm sense) to the measured non-equilibrated stress field, via the solution of an optimization problem. The extraction of the divergence-free (equilibrated) part of a general (non-equilibrated) field is performed using the Hodge decomposition of a symmetric matrix field, which is the generalization of the Helmholtz decomposition of a vector field into the sum of an irrotational field and a solenoidal field. The combination of: a) the Euler–Lagrange equations that solve the optimization problem, and b) the Hodge decomposition, gives a differential expression that contains the bi-harmonic operator and two times the curl operator acting on the experimental stress field. These high-order derivatives can be efficiently performed in Fourier space. The method is applied to filter the non-equilibrated parts of a synthetic piecewise constant stress fields with a known ground truth, and stress fields in Gum Metal, a beta-Ti-based alloy measured in-situ using Diffraction Contrast Tomography (DCT). In both cases, the largest corrections were obtained near grain boundaries.

36 MATERIALS SCIENCE↗
NASA NTRS1992

A real-time robot arm collision avoidance system

A data structure and update algorithm are presented for a prototype real-time collision avoidance safety system simulating a multirobot workspace. The data structure is a variant of the octree, which serves as a spatial index. An octree recursively decomposes 3D space into eight equal cubic octants until each octant meets some decomposition criteria. The N-objects octree, which indexes a collection of 3D primitive solids is used. These primitives make up the two (seven-degrees-of-freedom) robot arms and workspace modeled by the system. As robot arms move, the octree is updated to reflect their changed positions. During most update cycles, any given primitive does not change which octree nodes it is in. Thus, modification to the octree is rarely required. Cycle time for interpreting current arm joint angles, updating the octree to reflect new positions, and detecting/reporting imminent collisions averages 30 ms on an Intel 80386 processor running at 20 MHz.

Shaffer, Clifford A.↗
NASA NTRS1994

On the transition towards slow manifold in shallow-water and 3D Euler equations in a rotating frame

The long-time, asymptotic state of rotating homogeneous shallow-water equations is investigated. Our analysis is based on long-time averaged rotating shallow-water equations describing interactions of large-scale, horizontal, two-dimensional motions with surface inertial-gravity waves field for a shallow, uniformly rotating fluid layer. These equations are obtained in two steps: first by introducing a Poincare/Kelvin linear propagator directly into classical shallow-water equations, then by averaging. The averaged equations describe interaction of wave fields with large-scale motions on time scales long compared to the time scale 1/f(sub o) introduced by rotation (f(sub o)/2-angular velocity of background rotation). The present analysis is similar to the one presented by Waleffe (1991) for 3D Euler equations in a rotating frame. However, since three-wave interactions in rotating shallow-water equations are forbidden, the final equations describing the asymptotic state are simplified considerably. Special emphasis is given to a new conservation law found in the asymptotic state and decoupling of the dynamics of the divergence free part of the velocity field. The possible rising of a decoupled dynamics in the asymptotic state is also investigated for homogeneous turbulence subjected to a background rotation. In our analysis we use long-time expansion, where the velocity field is decomposed into the 'slow manifold' part (the manifold which is unaffected by the linear 'rapid' effects of rotation or the inertial waves) and a formal 3D disturbance. We derive the physical space version of the long-time averaged equations and consider an invariant, basis-free derivation. This formulation can be used to generalize Waleffe's (1991) helical decomposition to viscous inhomogeneous flows (e.g. problems in cylindrical geometry with no-slip boundary conditions on the cylinder surface and homogeneous in the vertical direction).

Mahalov, A.↗
DOE OSTI2023

Surface Properties of Double-Fin Generated Shock-Wave/Boundary-Layer Interactions

Shock-Wave/Boundary-Layer Interaction (SBLI) is ubiquitous in high-speed air vehicles. SBLI surface flowfield properties of crossing shocks induced by symmetric Double-Fins (DFs) at fin angles of 8° and 10° at Mach 2 are experimentally investigated; a 10° Single-Fin (SF) is also explored as a comparison. Surface visualization is used to capture distinct flowfield structures such as separation and upstream influence. Steady and unsteady Pressure-Sensitive Paints (PSPs) are used to obtain global surface pressure fields. Characteristics of DF-SBLI surface topology are discussed by comparing the corresponding SF-SBLI. Here, the effect of fin angle on DF-SBLI is characterized, and unsteady dynamics of the pressure field are examined. Spectral Proper Orthogonal Decomposition (SPOD) is performed on unsteady PSP, and traveling surface pressure waves and their frequency-dependent behavior are discussed. Dispersion relation of surface pressure waves is revealed by performing two-dimensional space–time Fourier transform on unsteady PSP, and the results are compared with the phase velocity distributions obtained from SPOD. Accompanying group velocity behavior is examined for distinct SBLI regions wherein wave propagation is found dependent on its frequency. Steady surface pressures along the centerline are compared with previous experimental data. Fin-tip spacing is found to be an essential parameter for scaling of upstream influence length.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRSDate not supplied

Next Steps: Laying the Groundwork for Bundle Protocol v7

Delay/Disruption Tolerant Networking (DTN) is a networking model and protocol suite that extends the terrestrial internet to the challenging communication environments of space. These environments are typically subject to frequent disruptions, which can cause delays or errors. DTN protects data transmission by wrapping data into bundles (similar to Internet Protocol packets), storing them until a connection can be established between two nodes (similar to terrestrial routers or computers), and forwarding them to their destinations. Bundle Protocol (BP) is responsible for generating those bundles and creates the transport layer of DTN, much like how Transmission Control Protocol (TCP) and User Datagram Protocol (UDP) create the transport layer of the Internet Protocol. BPv6 is the current, accepted version of the Bundle Protocol standard. However, recent missions and test implementations have revealed missing components and areas for improvement in the standard. Using lessons learned from NASA missions and gathering inspiration from the Internet Protocol, BPv7 is intended to be a more robust Bundle Protocol that improves upon its predecessor and increases the technology readiness level of the DTN architecture. The DTN Standard Interface Design team, a sub-team of the DTN Infusion Project at the Goddard Space Flight Center, worked to create a dictionary of terms for bundle components and functional decomposition of the protocol. These efforts aided in the standardization of BP interfaces, something missing from BPv6, and supported parallel network management and configuration work. This standardization will ultimately contribute to LunaNet (a lunar communications and navigation architecture that will bring networking, positioning, navigation, timing and science services to the Moon), the Solar System Internet (SSI), and expand crewed and uncrewed space exploration opportunities.

DTN↗
NASA NTRSDate not supplied

Next Steps: Laying the Groundwork for Bundle Protocol v7

Delay/Disruption Tolerant Networking (DTN) is a networking model and protocol suite that extends the terrestrial internet to the challenging communication environments of space. These environments are typically subject to frequent disruptions, which can cause delays or errors. DTN protects data transmission by wrapping data into bundles (similar to Internet Protocol packets), storing them until a connection can be established between two nodes (similar to terrestrial routers or computers), and forwarding them to their destinations. Bundle Protocol (BP) is responsible for generating those bundles and creates the transport layer of DTN, much like how Transmission Control Protocol (TCP) and User Datagram Protocol (UDP) create the transport layer of the Internet Protocol. BPv6 is the current, accepted version of the Bundle Protocol standard. However, recent missions and test implementations have revealed missing components and areas for improvement in the standard. Using lessons learned from NASA missions and gathering inspiration from the Internet Protocol, BPv7 is intended to be a more robust Bundle Protocol that improves upon its predecessor and increases the technology readiness level of the DTN architecture. The DTN Standard Interface Design team, a sub-team of the DTN Infusion Project at the Goddard Space Flight Center, worked to create a dictionary of terms for bundle components and functional decomposition of the protocol. These efforts aided in the standardization of BP interfaces, something missing from BPv6, and supported parallel network management and configuration work. This standardization will ultimately contribute to LunaNet (a lunar communications and navigation architecture that will bring networking, positioning, navigation, timing and science services to the Moon), the Solar System Internet (SSI), and expand crewed and uncrewed space exploration opportunities.

dtn↗
NASA NTRS2005

High-temperature catalyst for catalytic combustion and decomposition

A robust, high temperature mixed metal oxide catalyst for propellant composition, including high concentration hydrogen peroxide, and catalytic combustion, including methane air mixtures. The uses include target, space, and on-orbit propulsion systems and low-emission terrestrial power and gas generation. The catalyst system requires no special preheat apparatus or special sequencing to meet start-up requirements, enabling a fast overall response time. Start-up transients of less than 1 second have been demonstrated with catalyst bed and propellant temperatures as low as 50 degrees Fahrenheit. The catalyst system has consistently demonstrated high decomposition effeciency, extremely low decomposition roughness, and long operating life on multiple test particles.

Mays, Jeffrey A.↗
NASA NTRS1995

Optimization of Time-Dependent Particle Tracing Using Tetrahedral Decomposition

An efficient algorithm is presented for computing particle paths, streak lines and time lines in time-dependent flows with moving curvilinear grids. The integration, velocity interpolation and step-size control are all performed in physical space which avoids the need to transform the velocity field into computational space. This leads to higher accuracy because there are no Jacobian matrix approximations or expensive matrix inversions. Integration accuracy is maintained using an adaptive step-size control scheme which is regulated by the path line curvature. The problem of cell-searching, point location and interpolation in physical space is simplified by decomposing hexahedral cells into tetrahedral cells. This enables the point location to be done analytically and substantially faster than with a Newton-Raphson iterative method. Results presented show this algorithm is up to six times faster than particle tracers which operate on hexahedral cells yet produces almost identical particle trajectories.

Kenwright, David↗
NASA NTRS1981

Modeling hydrogen-cyanide absorption in fires

A mathematical model is developed for predicting blood concentrations of cyanide as functions of exposure time to constant levels of cyanide in the atmosphere. A toxic gas (which may form as a result of decomposition of combustion materials used in transportation vehicles) is breathed into the alveolar space and transferred from the alveolar space to the blood by a first-order process, dependent on the concentration of the toxicant in the alveolar space. The model predicts that blood cyanide levels are more sensitive to the breathing cycle than to blood circulation. A model estimate of the relative effects of CO and HCN atmospheres, generated in an experimental chamber with an epoxy polymer, shows that toxic effects of cyanide occur long before those of carbon monoxide.

Cagliostro, D. E.↗
DOE OSTI2022

Preventing Reverse Engineering of Critical Industrial Data with DIOD

Business analytics augmented by artificial intelligence and machine learning (AI/ML) have revolutionized the role of data in the modern world. In recent years, businesses have incorporated data into their decision-making process for better prediction, risk-assessment, content creation, etc. While such businesses often seek to leverage the full use of their data through third-party AI/ML services, they are often hampered by the risks of data leaks, reverse-engineering, stolen technology, etc. that often have disastrous consequences for businesses and their stakeholders alike. Thus, there arises a need for data masking prior to its transmission that obfuscates proprietary information while preserving the information relevant for AI/ML applications. In order to meet the needs of industrial data which are significantly different from those of data warehouses, previous work proposed an efficient time and space-scalable data masking paradigm known as the deceptive infusion of data (DIOD) methodology. The present work expands upon this work by leveraging existing reverse-engineering capabilities to facilitate the decomposition of industrial data into its proprietary and AI/ML-relevant parts, referred to as fundamental and inference metadata respectively. Both sets of metadata are further obfuscated in accordance with the DIOD methodology to create the DIOD rendition of the industrial data, which is rendered immune to reverse-engineering by discarding proprietary information and only preserving AI/ML-relevant information. Additionally, constraints of the original DIOD manuscript are relaxed using mutual information by configuring the methodology to the target AI/ML application to unlock the full potential of the DIOD methodology. As an example, data from a nuclear reactor is transformed into that from a nonlinear spring-mass system with different levels of data masking as required by the generic system and the target application.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2001

Performance of the Wavelet Decomposition on Massively Parallel Architectures

Traditionally, Fourier Transforms have been utilized for performing signal analysis and representation. But although it is straightforward to reconstruct a signal from its Fourier transform, no local description of the signal is included in its Fourier representation. To alleviate this problem, Windowed Fourier transforms and then wavelet transforms have been introduced, and it has been proven that wavelets give a better localization than traditional Fourier transforms, as well as a better division of the time- or space-frequency plane than Windowed Fourier transforms. Because of these properties and after the development of several fast algorithms for computing the wavelet representation of any signal, in particular the Multi-Resolution Analysis (MRA) developed by Mallat, wavelet transforms have increasingly been applied to signal analysis problems, especially real-life problems, in which speed is critical. In this paper we present and compare efficient wavelet decomposition algorithms on different parallel architectures. We report and analyze experimental measurements, using NASA remotely sensed images. Results show that our algorithms achieve significant performance gains on current high performance parallel systems, and meet scientific applications and multimedia requirements. The extensive performance measurements collected over a number of high-performance computer systems have revealed important architectural characteristics of these systems, in relation to the processing demands of the wavelet decomposition of digital images.

El-Ghazawi, Tarek A.↗
DOE OSTI2022

Conservative DG method for the micro-macro decomposition of the Vlasov–Poisson–Lenard–Bernstein model

The micro-macro (mM) decomposition approach is considered for the numerical solution of the Vlasov– Poisson–Lenard–Bernstein (VPLB) system, which is relevant for plasma physics applications. In the mM approach, the kinetic distribution function is decomposed as $f$ = $\mathscr{E}$[$ρ_f$] + g , where $\mathscr{E}$ is a local equilibrium distribution, depending on the macroscopic moments $ρ_f$ = $∫_{\mathbb{R}}$ $efdv$ = $\langle$$ef$$\rangle$$_{\mathbb{R}}$, where e = (1, $v$, $\frac{1}{2}$ $v^2$) T , and $g$, the microscopic distribution, is defined such that $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0. We aim to design numerical methods for the mM decomposition of the VPLB system, which consists of coupled equations for $ρ_f$ and $g$. To this end, we use the discontinuous Galerkin (DG) method for phase-space discretization, and implicit-explicit (IMEX) time integration, where the phase-space advection terms are integrated explicitly and the collision operator is integrated implicitly. We give special consideration to ensure that the resulting mM method maintains the $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0 constraint, which may be necessary for obtaining (i) satisfactory results in the collision dominated regime with coarse velocity resolution, and (ii) unambiguous conservation properties. The constraint-preserving property is achieved through a consistent discretization of the equations governing the micro and macro components. Here, we present numerical results that demonstrate the performance of the mM method. The mM method is also compared against a corresponding DG-IMEX method solving directly for $f$.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Space-Time Finite Element Tensor Network Approach for the Time-Dependent Convection–Diffusion–Reaction Equation with Variable Coefficients

In this paper, we present a new space-time Galerkin-like method, where we treat the discretization of spatial and temporal domains simultaneously. This method utilizes a mixed formulation of the tensor-train (TT) and quantized tensor-train (QTT) (please see Section Tensor-Train Decomposition), designed for the finite element discretization (Q1-FEM) of the time-dependent convection–diffusion–reaction (CDR) equation. We reformulate the assembly process of the finite element discretized CDR to enhance its compatibility with tensor operations and introduce a low-rank tensor structure for the finite element operators. Recognizing the banded structure inherent in the finite element framework’s discrete operators, we further exploit the QTT format of the CDR to achieve greater speed and compression. Additionally, we present a comprehensive approach for integrating variable coefficients of CDR into the global discrete operators within the TT/QTT framework. The effectiveness of the proposed method, in terms of memory efficiency and computational complexity, is demonstrated through a series of numerical experiments, including a semi-linear example.

convection–diffusion–reaction equation↗
DOE OSTI2020

Time-series learning of latent-space dynamics for reduced-order model closure

In this work, we study the performance of long short-term memory networks (LSTMs) and neural ordinary differential equations (NODEs) in learning latent-space representations of dynamical equations for an advection-dominated problem given by the viscous Burgers equation. Our formulation is devised in a nonintrusive manner with an equation-free evolution of dynamics in a reduced space with the latter being obtained through a proper orthogonal decomposition. In addition, we leverage the sequential nature of learning for both LSTMs and NODEs to demonstrate their capability for closure in systems that are not completely resolved in the reduced space. We assess our hypothesis for two advection-dominated problems given by the viscous Burgers equation. We observe that both LSTMs and NODEs are able to reproduce the effects of the absent scales for our test cases more effectively than does intrusive dynamics evolution through a Galerkin projection. This result empirically suggests that time-series learning techniques implicitly leverage a memory kernel for coarse-grained system closure as is suggested through the Mori–Zwanzig formalism.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A least-squares finite element method based on the Helmholtz decomposition for hyperbolic balance laws

In this paper, a least-squares finite element method for scalar nonlinear hyperbolic balance laws is proposed and studied. The approach is based on a formulation that utilizes an appropriate Helmholtz decomposition of the flux vector and is related to the standard notion of a weak solution. This relationship, together with a corresponding connection to negative-norm least-squares, is described in detail. As a consequence, an important numerical conservation theorem is obtained, similar to the famous Lax–Wendroff theorem. The numerical conservation properties of the method in this paper do not fall precisely in the framework introduced by Lax and Wendroff, but they are similar in spirit as they guarantee that when L 2 convergence holds, the resulting approximations approach a weak solution to the hyperbolic problem. The least-squares functional is continuous and coercive in an H -1 -type norm, but not L 2 -coercive. Nevertheless, the L 2 convergence properties of the method are discussed. Convergence can be obtained either by an explicit regularization of the functional, that provides control of the L 2 norm, or by properly choosing the finite element spaces, providing implicit control of the L 2 norm. Numerical results for the inviscid Burgers equation with discontinuous source terms are shown, demonstrating the L 2 convergence of the obtained approximations to the physically admissible solution. The numerical method utilizes a least-squares functional, minimized on finite element spaces, and a Gauss–Newton technique with nested iteration. Finally, we believe that the linear systems encountered with this formulation are amenable to multigrid techniques and combining the method with adaptive mesh refinement would make this approach an efficient tool for solving balance laws (this is the focus of a future study).

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2004

Design and assembly of a catalyst bed gas generator for the catalytic decomposition of high concentration hydrogen peroxide propellants and the catalytic combustion of hydrocarbon/air mixtures

A method for designing and assembling a high performance catalyst bed gas generator for use in decomposing propellants, particularly hydrogen peroxide propellants, for use in target, space, and on-orbit propulsion systems and low-emission terrestrial power and gas generation. The gas generator utilizes a sectioned catalyst bed system, and incorporates a robust, high temperature mixed metal oxide catalyst. The gas generator requires no special preheat apparatus or special sequencing to meet start-up requirements, enabling a fast overall response time. The high performance catalyst bed gas generator system has consistently demonstrated high decomposition efficiency, extremely low decomposition roughness, and long operating life on multiple test articles.

Lohner, Kevin A.↗
DOE OSTI2025

Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach

Ground state energy estimation in physical, chemical, and materials sciences is one of the most promising applications of quantum computing. In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting real-time measurements and post-processing them using the machinery of dynamic mode decomposition (DMD). From the perspective of quantum dynamics, we establish that our approach can be formally understood as a stable variational method on the function space of observables available from a quantum many-body system. We also provide strong theoretical and numerical evidence that our method converges rapidly even in the presence of a large degree of perturbative noise, and show that the method bears an isomorphism to robust matrix factorization methods developed independently across various scientific communities. Our numerical benchmarks on spin and molecular systems demonstrate an accelerated convergence and a favorable resource reduction over state-of-the-art algorithms. The DMD-centric strategy can systematically mitigate noise and stands out as a leading hybrid quantum-classical eigensolver.

Shen, Yizhi↗
NASA NTRS1976

Solar photochemistry using the space shuttle

A continuing source of difficulty in cometary astrophysics is understanding the origin of C2, C3, NH and CO(+) species in comets. An experiment is proposed to investigate these problems by continuously releasing suspected parent gases from the space shuttle and using a dye laser to selectively excite fragments produced as a result of solar photochemical decomposition of the molecules. The backscattered fluorescence is gathered by a telescope, spectrally filtered, and measured as a function of time after the laser pulse.

Jackson, W. M.↗