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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A multiresolution adaptive wavelet method for nonlinear partial differential equations

We report the multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to solve partial differential equations (PDEs) with features evolving on a wide range of spatial and temporal scales. To meet these challenges, we present a multiresolution wavelet algorithm to solve PDEs with significant data compression and explicit error control. We discretize in space by projecting fields and spatial derivative operators onto wavelet basis functions. We provide error estimates for the wavelet representation of fields and their derivatives. Then, our estimates are used to construct a sparse multiresolution discretization which guarantees the prescribed accuracy. Additionally, we embed a predictor-corrector procedure within the temporal integration to dynamically adapt the computational grid and maintain the accuracy of the solution of the PDE as it evolves. We present examples to highlight the accuracy and adaptivity of our approach.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

Real-time optical laboratory solution of parabolic differential equations

An optical laboratory matrix-vector processor is used to solve parabolic differential equations (the transient diffusion equation with two space variables and time) by an explicit algorithm. This includes optical matrix-vector nonbase-2 encoded laboratory data, the combination of nonbase-2 and frequency-multiplexed data on such processors, a high-accuracy optical laboratory solution of a partial differential equation, new data partitioning techniques, and a discussion of a multiprocessor optical matrix-vector architecture.

Casasent, David↗
DOE OSTI2020

Gravitational Contact Interactions and the Physical Equivalence of Weyl Transformations in Effective Field Theory

Theories of scalars and gravity, with non-minimal interactions, $\sim (M_P^2 +F(\phi) )R +L(\phi)$, have graviton exchange induced contact terms. These terms arise in single particle reducible diagrams with vertices $\propto q^2$ that cancel the Feynman propagator denominator $1/q^2$ and are familiar in various other physical contexts. In gravity these lead to additional terms in the action such as $\sim F(\phi) T_\mu^\mu(\phi)/M_P^2$ and $F(\phi)\partial^2 F(\phi)/M_P^2$. The contact terms are equivalent to induced operators obtained by a Weyl transformation that removes the non-minimal interactions, leaving a minimal Einstein-Hilbert gravitational action. This demonstrates explicitly the equivalence of different representations of the action under Weyl transformations, both classically and quantum mechanically. To avoid such "hidden contact terms" one is compelled to go to the minimal Einstein-Hilbert representation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

A Robust Methodology to Elucidate Kinetics of Room Temperature Electrochemical Propane Adsorption on Platinum

Electrocatalytic activation of alkanes can further decarbonize chemical manufacturing by leveraging affordable renewable electricity and readily available shale gas reserves in the United States. Earlier works have identified the unique role of Pt in adsorbing and activating alkanes, like propane, at room temperature in acidic, aqueous electrolytes, revealing spontaneous formation of deeply dehydrogenated propane-derived surface species with an intact C 3 - backbone. Although an adsorption mechanism was hypothesized, it has not been explicitly investigated to date, preventing the quantification of kinetic rate parameters. A robust methodology to investigate and benchmark propane adsorption kinetics on Pt is critical for the rational design of electrocatalysts that exhibit higher selectivity toward desired partially oxidized products. Herein, we analyze an oxidative current transience that appears during the adsorption of propane on Pt in aqueous electrochemical conditions and develop a methodology that elucidates the adsorption mechanism and enables quantification of rate parameters such as order dependences and apparent activation barriers. This method yields an expected first-order dependence with respect to propane concentration at low coverage and reveals a second-order dependence with respect to the concentration of surface active sites. Additionally, the apparent activation barrier for propane adsorption was calculated using an Arrhenius analysis of the current transience under temperature control. The experimentally measured activation barrier of 35 kJ mol –1 is in excellent agreement with the theoretical barrier calculated by density functional theory (DFT). The kinetic analysis was extended, via the use of transition state theory, to extract entropy and enthalpy of activation, yielding consistent results with the proposed two-step adsorption mechanism and DFT calculations. These results demonstrate reliable quantification of kinetic parameters for electrocatalytic activation of C–H bonds in alkanes that can be employed for rational catalyst development for a versatile range of electrocatalytic conditions.

alkane activation↗
DOE OSTI2021

Theory and application of the vector pair correlation function for real-space crystallographic analysis of order/disorder correlations from STEM images

Deviations of local structure and chemistry from the average crystalline unit cell are increasingly recognized to have a significant influence on the properties of many technologically important materials. Here, we present the vector pair correlation function (vPCF) as a new real-space crystallographic analysis method, which can be applied to atomic-resolution scanning transmission electron microscopy (STEM) images to quantify and analyze structural order/disorder correlations. Our STEM-based vPCFs have several advantages over radial PCFs and/or 3D pair distribution functions from x-ray total scattering: vPCFs explicitly retain crystallographic orientation information, are spatially resolved, can be applied directly on a sublattice basis, and are suitable for any material that can be imaged with STEM. To show the utility of our approach, we measure partial vPCFs in Ba 5 SmSn 3 Nb 7 O 30 (BSSN), a tetragonal tungsten bronze (TTB) structured complex oxide. Many TTBs are known to be classical or relaxor ferroelectrics, and these properties have been correlated with the presence of superlattice ordering. BSSN, specifically, exhibits relaxor behavior and an incommensurate structural modulation. From the vPCF data, we observe that, of the cation sites, only the Ba (A2) sublattice is structurally modulated. We then infer the local modulation vector and reveal a marked anisotropy in its correlation length. Finally, short-range correlated polar displacements on the B2 cation sites are observed. This work introduces the vPCF as a powerful real-space crystallography technique, which enables direct, robust quantification of short-to-long range order on a sublattice-specific basis and is applicable to a wide range of complex material types.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1996

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for Aircraft Acoustic Nacelle Design

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Baumeister, Kenneth J.↗
NASA NTRS1996

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Baumeister, K. J.↗
NASA NTRS1978

A comparison of the Method of Lines to finite difference techniques in solving time-dependent partial differential equations

Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.

Kurtz, L. A.↗
NASA NTRS1993

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.

Farhat, Charbel↗
DOE OSTI2023

Parallel Algebraic Multigrid for Fusion and Higher-Order PDEs

Multigrid methods play a key role in large-scale scientific simulation because they are among the fastest and most scalable approaches for solving the underlying sparse linear systems of equations that arise from a wide array of Partial Differential Equation (PDE) discretizations. Algebraic multigrid (AMG) is a special type of multigrid method that depends only on the description of the linear system, giving it better portability and broader applicability than geometric multigrid, as it requires no explicit knowledge of the problem geometry. Even though these methods are widely used today, there are still applications where further development is needed. In this report, we focus on PDEs with higher-order terms (e.g., fourth order), concentrating on a PDE that arises in tokamak edge plasma simulations (a tokamak is a machine that confines a plasma using magnetic fields and is believed to be the leading plasma confinement concept for future fusion power plants). General multigrid relaxes a linear system on coarser grids and reverses this process with interpolation, but standard AMG methods struggle with the aforementioned higher-order PDEs. We investigate cyclic coarsening and interpolation heuristics, as well as new iterative approximation methods of refining the solution at each grid to improve the existing multigrid approach. To this end, we ensure that these techniques are transferable to a parallelized setting with LLNL’s supercomputers.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2009

Improved Model of a Mercury Ring Damper

A short document discusses the general problem of mathematical modeling of the three-dimensional rotational dynamics of rigid bodies and of the use of Euler parameters to eliminate the singularities occasioned by the use of Euler angles in such modeling. The document goes on to characterize a Hamiltonian model, developed by the authors, that utilizes the Euler parameters and, hence, is suitable for use in computational simulations that involve arbitrary rotational motion. In this formulation unlike in prior Euler-parameter-based formulations, there are no algebraic constraints. This formulation includes a general potential energy function, incorporates a minimum set of momentum variables, and takes an explicit state-space form convenient for numerical implementation. Practical application of this formulation has been demonstrated by the development of a new and simplified model of the rotational motion of a rigid rotor to which is attached a partially filled mercury ring damper. Models like this one are used in guidance and control of spin-stabilized spacecraft and gyroscope-stabilized seekers in guided missiles.

Fahrenthold, Eric P.↗
NASA NTRS1985

A mathematical formulation of the Scole control problem, part 1

A mathematical formulation of the SCOLE control problem in terms of a continuous model described by partial differential equations with delta functions on the boundary is presented along with three techniques of solution. The abstract wave equation approach leads immediately to a linear feedback law that can ensure (strong) stability. The boundary control approach yields an explicit solution, albeit in a simple case.

Balakrishnan, A. V.↗
DOE OSTI2024

SCIMON: Scientific Inspiration Machines Optimized for Novelty

We explore and enhance the ability of neu- ral language models to generate novel scien- tific directions grounded in literature. Work on literature-based hypothesis generation has traditionally focused on binary link prediction— severely limiting the expressivity of hypothe- ses. This line of work also does not focus on optimizing novelty. We take a dramatic depar- ture with a novel setting in which models use as input background contexts (e.g., problems, experimental settings, goals), and output natu- ral language ideas grounded in literature. We present SCIMON, a modeling framework that uses retrieval of “inspirations” from past scien- tific papers, and explicitly optimizes for novelty by iteratively comparing to prior papers and up- dating idea suggestions until sufficient novelty is achieved. Comprehensive evaluations reveal that GPT-4 tends to generate ideas with over- all low technical depth and novelty, while our methods partially mitigate this issue. Our work represents a first step toward evaluating and developing language models that generate new ideas derived from the scientific literature.

Ji, Heng↗
NASA NTRS2019

Influence of Strain-Gage Balance Characteristics on the Precision Error of the Drag Coefficient

Improvements and results of a new method are presented that computes a pre-test estimate of the precision error of the drag coefficient of a wind tunnel model. The error estimate is defined as the part of the drag coefficient's precision error that is primarily associated with the precision error of the angle of attack measurement and physical characteristics of the chosen strain-gage balance. The method indirectly describes the precision error of the angle of attack measurement by using an assumed balance gage output variation of one microV/V. The physical characteristics of the balance, on the other hand, are described by partial derivatives of the axial and normal forces with respect to the strain-gage outputs. These derivatives can directly be obtained from the data reduction matrix of the balance. The precision error estimate itself is calculated by applying a simple explicit equation that uses the model reference area, the dynamic pressure, the angle of attack, the coefficients of the linear terms of the data reduction matrix, and the electrical output variation of one microvolt per volt as input. Precision errors at constant angle of attack may be visualized as contour plots by plotting them, for example, versus the Mach number and the total pressure. Characteristics of NASA's MC60E balance are used in combination with the reference area of a generic wind tunnel model in order to demonstrate that error estimates are independent of both the balance load format and the units chosen for the description of balance loads, model reference area, and the dynamic pressure. Finally, experimental data from a wind tunnel test of the Ames Check Standard Model in the NASA Ames 11-foot Transonic Wind Tunnel illustrates the application of the method to real-world test data.

precision error↗
DOE OSTI2022

Matching Complexes of Trees and Applications of the Matching Tree Algorithm

A matching complex of a simple graph G is a simplicial complex with faces given by the matchings of G. The topology of matching complexes is mysterious; there are few graphs for which the homotopy type is known. Marietti and Testa showed that matching complexes of forests are contractible or homotopy equivalent to a wedge of spheres. We study two specific families of trees. For caterpillar graphs, we give explicit formulas for the number of spheres in each dimension and for perfect binary trees we find a strict connectivity bound. We also use a tool from discrete Morse theory called the Matching Tree Algorithm to study the connectivity of honeycomb graphs, partially answering a question raised by Jonsson.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Machine-learning based model reduction for partial differential equations

We develop a novel synergistic approach between model reduction and machine learning. The specific goal of this project is to aid in the construction of reduced order models for basis functions that are custom-made to represent the solution of partial differential equations. Partial differential equations (PDEs) are one of the main mathematical tools for describing physical phenomena. However, due to either efficiency or necessity, for many real-world problems, we are interested in constructing reduced order models (ROMs) which focus only on the explicit computation of subsets of the active spatio-temporal scales in the problem, while treating the interaction with the rest of the scales approximately. The task of accurate representation of such interactions (usually called memory terms) constitutes a vast area of research known as model reduction. PI Stinis has significant expertise in the construction of ROMs for complex systems. In addition, in recent work with the project key participant Qadeer, they have utilized machine learning to acquire custom-made basis functions (CBFs) to expand the solutions of PDEs. In the proposed work, we will merge the two concepts by constructing ROMs for subsets of the CBFs needed to represent the solution of a PDE. Specifically, we will use the Mori-Zwanzig model reduction formalism to construct ROMs for subsets of CBFs for nonlinear PDEs of various complexity, as well as investigate the usage of CBFs in the spectral vanishing viscosity method for problems that can form shocks in finite time. The outcome of the research is aimed to be proof-of-concept about a novel synergistic approach between model reduction and machine learning, thus advancing the field of scientific machine learning. Such a capability will benefit the efficient modeling of physical systems appearing in various areas of interest to the DOE.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Analysis of Issues for Project Scheduling by Multiple, Dispersed Schedulers (distributed Scheduling) and Requirements for Manual Protocols and Computer-based Support

Although computerized operations have significant gains realized in many areas, one area, scheduling, has enjoyed few benefits from automation. The traditional methods of industrial engineering and operations research have not proven robust enough to handle the complexities associated with the scheduling of realistic problems. To address this need, NASA has developed the computer-aided scheduling system (COMPASS), a sophisticated, interactive scheduling tool that is in wide-spread use within NASA and the contractor community. Therefore, COMPASS provides no explicit support for the large class of problems in which several people, perhaps at various locations, build separate schedules that share a common pool of resources. This research examines the issue of distributing scheduling, as applied to application domains characterized by the partial ordering of tasks, limited resources, and time restrictions. The focus of this research is on identifying issues related to distributed scheduling, locating applicable problem domains within NASA, and suggesting areas for ongoing research. The issues that this research identifies are goals, rescheduling requirements, database support, the need for communication and coordination among individual schedulers, the potential for expert system support for scheduling, and the possibility of integrating artificially intelligent schedulers into a network of human schedulers.

Richards, Stephen F.↗