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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 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Modelling a particular class of stochastic systems

In this paper a method is given for obtaining a mathematical model of a class of black boxes having multiple inputs and multiple outputs in terms of Ito stochastic integral equations. This method is applicable to the class of black boxes having ergodic correlation functions when there is zero applied input. The point of view adopted in this paper is phenomenological in that it is desired that calculations made using the mathematical model should be 'close' to what is actually observed at the output of the black box.

Eyman, E. D.↗
NASA NTRS1973

Modeling a particular class of multiple-input/multiple-output black boxes with stochastic integral equations and identifying the required parameters

A method is given for obtaining a mathematical model of a class of black boxes having multiple inputs and multiple outputs in terms of Ito stochastic integral equations. This method is applicable to the class of black boxes having ergodic correlation functions when there is zero applied input. The point of view adopted in this paper is phenomenological in that it is desired that calculations made using the mathematical model should be close to what is actually observed at the output of the black box. How close is defined in the problem statement.

Eyman, E. D.↗
DOE OSTI2020

Verification benchmarks for single-phase flow in three-dimensional fractured porous media

Flow in fractured porous media occurs in the earth’s subsurface, in biological tissues, and in man-made materials. Fractures have a dominating influence on flow processes, and the last decade has seen an extensive development of models and numerical methods that explicitly account for their presence. To support these developments, four benchmark cases for single-phase flow in three-dimensional fractured porous media are presented. Furthermore, the cases are specifically designed to test the methods’ capabilities in handling various complexities common to the geometrical structures of fracture networks. Based on an open call for participation, results obtained with 17 numerical methods were collected. This paper presents the underlying mathematical model, an overview of the features of the participating numerical methods, and their performance in solving the benchmark cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Exact closed-form unitary transformations of fermionic operators

Unitary transformations play a fundamental role in many-body physics, and except for special cases, they are not expressible in closed form. We present closed-form expressions for unitary transformations generated by a single fermionic operator for Hermitian and anti-Hermitian generators. We demonstrate the usefulness of these expressions in formal analyses of unitary transformations and numerical applications to Hamiltonian downfolding in quantum computing and Heisenberg dynamics. Furthermore, this work paves the way for new analytical treatments of unitary transformations and numerical many-body methods for fermions.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS2005

Formal Requirements-Based Programming for Complex Systems

Computer science as a field has not yet produced a general method to mechanically transform complex computer system requirements into a provably equivalent implementation. Such a method would be one major step towards dealing with complexity in computing, yet it remains the elusive holy grail of system development. Currently available tools and methods that start with a formal model of a system and mechanically produce a provably equivalent implementation are valuable but not sufficient. The gap that such tools and methods leave unfilled is that the formal models cannot be proven to be equivalent to the system requirements as originated by the customer For the classes of complex systems whose behavior can be described as a finite (but significant) set of scenarios, we offer a method for mechanically transforming requirements (expressed in restricted natural language, or appropriate graphical notations) into a provably equivalent formal model that can be used as the basis for code generation and other transformations. While other techniques are available, this method is unique in offering full mathematical tractability while using notations and techniques that are well known and well trusted. We illustrate the application of the method to an example procedure from the Hubble Robotic Servicing Mission currently under study and preliminary formulation at NASA Goddard Space Flight Center.

Rash, James L.↗
NASA NTRS2018

Lebedev Scheme for Ultrasound Simulation in Composites

The growing use of composite materials for aerospace applications has resulted in a need for quantitative nondestructive evaluation (NDE) methods appropriate for characterizing damage in composite components. NDE simulation tools, such as ultrasound models, can aid in enabling optimized inspection methods and establishing confidence in inspection capabilities. In this paper, a mathematical approach using the Lebedev Finite Difference (LFD) method is presented for ultrasonic wave simulation in composites. Boundary condition equations for implementing stress-free boundaries (necessary for simulation of NDE scenarios) are also presented. Quantitative comparisons between LFD guided wave ultrasound simulation results, experimental guided wave data, and dispersion curves are described. Additionally, stability tests are performed to establish the LFD code behavior in the presence of stress-free boundaries and low-symmetry anisotropy. Results show that LFD is an appropriate approach for simulating ultrasound in anisotropic composite materials and that the method is stable in the presence of low-symmetry anisotropy and stress-free boundaries. Studies presented in this paper include guided wave simulation in hexagonal, monoclinic, triclinic and layered composite laminates.

Guided wave↗
DOE OSTI2023

Practical Guide to Chemometric Analysis of Optical Spectroscopic Data

The methodology and mathematical treatment of several classic multivariate methods for the analysis of spectroscopic data is demonstrated in a straightforward way that can be used as a basis for teaching an undergraduate introductory course on chemometric analysis. The multivariate techniques of classical least squares (CLS), principal component regression (PCR), and partial least squares (PLS), as well as the univariate Beer’s law method have been described and compared, building students’ understanding by starting with the univariate method and progressing step by step into the multivariate methods. Equations for the production of regression vectors from training set spectral data is described and their use demonstrated for the prediction of constituent concentrations on a separate validation set of spectra. Extreme care is taken to ensure consistency in variable formatting of data matrices. This provides a key foundation to understanding how spectral data are manipulated using these different mathematical approaches for building quantitative regression models. Each method is applied to a real-world data set, and the results are discussed to show students the types of information that can be gleaned from each method. A training set comprised of 20 infrared absorbance spectra containing 3 constituents (benzene, polystyrene, and gasoline) of known composition are used to demonstrate the matrix operations for each regression method. A separate set of 12 real-world napalm samples (containing benzene, polystyrene and gasoline) are used as a validation set to demonstrate the ability to utilize the regression models on an unknown dataset. A toolbox (PNNL Chemometric Toolbox) written in MATLAB language is supplied in the Supplemental Information file and can be used as a companion for understanding the development and deployment of the chemometric algorithms described in this paper. The datasets of the infrared spectra are also supplied, allowing users to build and inspect the chemometric models on their own. Finally, the Toolbox includes scripts to assist users in loading their own datasets into MATLAB and performing CLS, PCR, and PLS on their data.

Upper-Division Undergraduate, Analytical Chemistry↗
NASA NTRS1992

Enhanced Method Of Reduction Of Dynamical Models

Enhanced projection-and-assembly method is recent product of efforts to model mathematically dynamics of vibrations of large, flexible structures. In projection-and-assembly method modes contributing significantly to control input and output points selected at system (overall structure) level, then projected (in abstract mathematical sense) onto components of system. In enhanced version, static correction modes capture static contributions of those modes neglected in reduced-order model. Reduced models for suppressing vibrations of structures made more accurate.

Lee, Allan Y.↗
DOE OSTI2021

Galvanostatic Intermittent Titration Technique Reinvented: Part I. A Critical Review

The galvanostatic intermittent titration technique (GITT), introduced in 1977 by Weppner and Huggins, provided a readily accessible means to measuring the chemical diffusion coefficient of electrochemical electrode materials. The method continues to be widely used today, but the reported diffusivity values are highly inconsistent, ranging as much as four orders of magnitude for some Li layered oxide compositions. Even qualitative trends of diffusivity are inconsistent, suggesting significant flaws in the implementation of the method. Other variants of the GITT method also suffer from similar inconsistency problems. Here we identify numerous sources of significant error including composition-dependent reaction overpotentials, mathematical flaws in the relaxation analysis methods, finite-size and non-planar geometry effects, inter-particle inhomogeneity issues, early transient effects, and surface area uncertainties. We propose a simple relaxation analysis scheme using the time variable t relax + τ - t relax , where t relax is relaxation time and τ is the galvanostatic pulse duration. We also propose to use dense diffusion-limited samples to isolate the bulk-diffusion process in the time domain. Chemical diffusivity can be extracted much more reliably with this improved implementation of the GITT method.

25 ENERGY STORAGE↗
NASA NTRS2007

A Fast Method of Deriving the Kirchhoff Formula for Moving Surfaces

The Kirchhoff formula for a moving surface is very useful in many wave propagation problems, particularly in the prediction of noise from rotating machinery. Several publications in the last two decades have presented derivations of the Kirchhoff formula for moving surfaces in both time and frequency domains. Here we present a method originally developed by Farassat and Myers in time domain that is both simple and direct. It is based on generalized function theory and the useful concept of imbedding the problem in the unbounded three-dimensional space. We derive an inhomogeneous wave equation with the source terms that involve Dirac delta functions with their supports on the moving data surface. This wave equation is then solved using the simple free space Green's function of the wave equation resulting in the Kirchhoff formula. The algebraic manipulations are minimal and simple. We do not need the Green's theorem in four dimensions and there is no ambiguity in the interpretation of any terms in the final formulas. Furthermore, this method also gives the simplest derivation of the classical Kirchhoff formula which has a fairly lengthy derivation in physics and applied mathematics books. The Farassat-Myers method can be used easily in frequency domain.

Farassat, F.↗
DOE OSTI2025

Development of Accelerated Kinetic Monte Carlo Code for Simulation of Helium Bubble Evolution

A mesoscale model to predict helium bubble evolution is needed for tritium applications. Such a model requires that the conventional kinetic Monte Carlo (kMC) simulations be significantly accelerated. The objective of this report is to (a) highlight the concepts and mathematical expressions of the accelerated method for defect implementation that have not been published, (b) show an example input file to run the kMC code, and (c) provide suggestions on future improvement following my retirement.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

On the Optimal Stabilization of an Integral Manifold

By the method of Lyapunov functions, we study the problem of optimal stabilization of an analytically defined integral manifold in the class of stochastic differential equations in the case where random perturbations belong to the class of processes with independent increments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

A simple finite element method for non-divergence form elliptic equation

Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Disaster risk and artificial intelligence: A framework to characterize conceptual synergies and future opportunities

Artificial intelligence (AI) methods have revolutionized and redefined the landscape of data analysis in business, healthcare, and technology. These methods have innovated the applied mathematics, computer science, and engineering fields and are showing considerable potential for risk science, especially in the disaster risk domain. The disaster risk field has yet to define itself as a necessary application domain for AI implementation by defining how to responsibly balance AI and disaster risk. (1) How is AI being used for disaster risk applications; and how are these applications addressing the principles and assumptions of risk science, (2) What are the benefits of AI being used for risk applications; and what are the benefits of applying risk principles and assumptions for AI-based applications, (3) What are the synergies between AI and risk science applications, and (4) What are the characteristics of effective use of fundamental risk principles and assumptions for AI-based applications? This study develops and disseminates an online survey questionnaire that leverages expertise from risk and AI professionals to identify the most important characteristics related to AI and risk, then presents a framework for gauging how AI and disaster risk can be balanced. This study is the first to develop a classification system for applying risk principles for AI-based applications. This classification contributes to understanding of AI and risk by exploring how AI can be used to manage risk, how AI methods introduce new or additional risk, and whether fundamental risk principles and assumptions are sufficient for AI-based applications.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2004

Design and Experimental Verification of Deployable/Inflatable Ultra-Lightweight Structures

Because launch cost of a space structural system is often proportional to the launch volume and mass and there is no significant gravity in space, NASA's space exploration programs and various science missions have stimulated extensive use of ultra-lightweight deployable/inflatable structures. These structures are named here as Highly Flexible Structures (HFSs) because they are designed to undergo large displacements, rotations, and/or buckling without plastic deformation under normal operation conditions. Except recent applications to space structural systems, HFSs have been used in many mechanical systems, civil structures, aerospace vehicles, home appliances, and medical devices to satisfy space limitations, provide special mechanisms, and/or reduce structural weight. The extensive use of HFSs in today's structural engineering reveals the need of a design and analysis software and a database system with design guidelines for practicing engineers to perform computer-aided design and rapid prototyping of HFSs. Also to prepare engineering students for future structural engineering requires a new and easy-to- understand method of presenting the complex mathematics of the modeling and analysis of HFSs. However, because of the high flexibility of HFSs, many unique challenging problems in the modeling, design and analysis of HFSs need to be studied. The current state of research on HFSs needs advances in the following areas: (1) modeling of large rotations using appropriate strain measures, (2) modeling of cross-section warpings of structures, (3) how to account for both large rotations and cross- section warpings in 2D (two-dimensional) and 1D structural theories, (4) modeling of thickness thinning of membranes due to inflation pressure, pretension, and temperature change, (5) prediction of inflated shapes and wrinkles of inflatable structures, (6) development of efficient numerical methods for nonlinear static and dynamic analyses, and (7) filling the gap between geometrically exact elastic analysis and elastoplastic analysis. The objectives of this research project were: (1) to study the modeling, design, and analysis of deployable/inflatable ultra-lightweight structures, (2) to perform numerical and experimental studies on the static and dynamic characteristics and deployability of HFSs, (3) to derive guidelines for designing HFSs, (4) to develop a MATLAB toolbox for the design, analysis, and dynamic animation of HFSs, and (5) to perform experiments and establish an adequate database of post-buckling characteristics of HFSs.

Pai, P. Frank↗
DOE OSTI2025

Position Papers for Inverse Methods for Complex Systems under Uncertainty Workshop

The ability to solve inverse problems – inferring unknown parameters, structures, or states of a system from observed data – is essential for advancing scientific discovery and innovation capabilities for the DOE mission. Basic research needs and challenges are particularly acute in emerging areas such as the interactive, data-driven, modeling and simulation of digital twins; decision support for experiments at DOE scientific user facilities; and for other complex systems and workflows. Inverse problems are at the heart of understanding and controlling complex systems due to factors such as observational data with varying modalities and fidelities, inherent uncertainties in physical measurements and numerical models, and the computational demands of rapid and high-fidelity simulations. The convergence of recent scientific computing trends – scientific machine learning, artificial intelligence, and computing advances such as exascale computing – is creating unprecedented opportunities. These advancements offer the potential to revolutionize how we approach inverse problems to extract actionable insights with the required level of accuracy and computational efficiency. This workshop and the Call for Position Papers are vital steps in bringing together experts to collectively explore and identify the new computational and mathematical directions needed in inverse methods for complex systems under uncertainty.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Comment on “Additional Insights Between Fermi-Löwdin Orbital SIC and the Localization Equation Constraints in SIC-DFT”

In a recent Letter, Aquino and Wong (AW) analyze the connection between the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) and the traditional Perdew– Zunger self-interaction correction (PZ-SIC) methods. In this work, the authors present a derivation of the conditions required to minimize the SIC density functional theory (DFT) total energy in FLO-SIC. These involve the gradient of the energy with respect to parameters known as Fermi-orbital descriptors (FODs) (called orbital “centroids” in ref 1) that are used together with the total charge density to determine the Fermi- Löwdin orbitals (FLOs). AW state that the conditions, the vanishing of the FOD gradient components, “resemble” the localization equations (LE), the minimum energy conditions in traditional PZ-SIC. The LE involve the equality of certain off-diagonal matrix elements of different orbital-dependent Hamiltonians. While AW are careful to say that their equations do not prove the mathematical equivalence of the two methods, the discussion in the text and the graphical table of contents figure suggest that vanishing FOD gradients imply satisfaction of the LE and vice versa, and hence that the methods are equivalent. We believe this ambiguity clouds an important issue, rather than clarifying it.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗