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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Calculation of the First Moment of Energy Using D-T Reactivity Formalisms Under the Maxwell-Boltzmann Distribution (Pt. 1)

Nuclear fusion science is an example of a scientific field with a rich history of expert involvement and scientific publications, which together, form an expert-knowledge base. One example of this history is the utilization of published reaction rates from a variety of authors. Investigators for Deuterium-Tritium (D-T) ion fusion can choose from using frequently cited methods: the Bosch and Hale reactivity, thermonuclear reaction rates from Caughlan and Fowler, and the reactivity evaluation from Miley, Towner & Ivich which forms the basis of the Naval Research Lab (NRL) formulary. There are other choices available. Each of the reactivity formulations considered here, are based upon the Maxwell- Boltzmann velocity distribution for D-T fusion ion reactants. Numerical methods for computer codes simulating hot, energetic plasmas, include tabulations of the reactivity, and the first moment of energy. The purpose of this study is to answer the question: what is the first moment of energy, and how has it been formulated? This report is part of a series of reports by the authors on D-T fusion-reaction formalism. The present focus is on defining the mathematical relationship of the first moment of D-T fusion ion kinetic energy, $\langle$E$\rangle$, with the fusion crosssection, fusion reactivity and its derivative with respect to ion-temperature. Three variants of the first moment $\langle$E$\rangle$ are analytically developed and explored: 1) constant cross-section, 2) a normalized first moment, and 3) a particular function of the first moment. Much of the mathematical development is relegated to the Appendices, for a concise presentation of topics and results. A research component of this discussion is our comparison of some of the reactivity and its derivative results between evaluations (1) versus (2) and (3), which the authors have not found in any other publication to date. This investigation is useful for validation, verification (V&V) and uncertainty quantification (UQ) as it compares the work of several authors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Computing Edge States without Hard Truncation

We present a numerical method which accurately computes the discrete spectrum and associated bound states of semi-infinite Hamiltonians which model electronic “edge” states localized at boundaries of one- and two-dimensional crystalline materials. The problem is nontrivial since arbitrarily large finite “hard” (Dirichlet) truncations of the Hamiltonian in the infinite bulk direction tend to produce spurious bound states partially supported at the truncation. Our method, which overcomes this difficulty, is to compute the Green's function of the semi-infinite Hamiltonian by imposing an appropriate boundary condition in the bulk direction; then, the spectral data is recovered via Riesz projection. We demonstrate our method's effectiveness by studies of edge states at a graphene zig-zag edge in the presence of defects modeled both by a discrete tight-binding model and a continuum PDE model under finite difference discretization. Our method may also be used to study states localized at domain wall-type edges in one- and two-dimensional materials where the edge Hamiltonian is infinite in both directions; we demonstrate this for the case of a tight-binding model of distinct honeycomb structures joined along a zig-zag edge. Here, we expect our method to be useful for designing novel devices based on precise wave-guiding by edge states.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{PT}$- and supersymmetric potential

In this work, we present trapped solitary wave solutions of a coupled nonlinear Schrödinger (NLS) system in 1 + 1 dimensions in the presence of an external, supersymmetric and complex $\mathcal{PT}$-symmetric potential. The Schrödinger system this work focuses on possesses exact solutions whose existence, stability, and spatio-temporal dynamics are investigated by means of analytical and numerical methods. Two different variational approximations are considered where the stability and dynamics of the solitary waves are explored in terms of eight and twelve time-dependent collective coordinates (CCs). We find regions of stability for specific potential choices as well as analytic expressions for the small oscillation frequencies in the CC approximation. Our findings are further supported by performing systematic numerical simulations of the NLS system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Can the Distance–Redshift Relation be Determined from Correlations between Luminosities?

We explore whether an independent determination of the distance–redshift relation, and hence cosmological model parameters, can be obtained from the apparent correlations between two different wave-band luminosities or fluxes, as has been claimed in recent works using the X-ray and ultraviolet luminosities and fluxes of quasars. We show that such an independent determination is possible only if the correlation between luminosities is obtained independently of the cosmological model and measured fluxes and redshifts, for example, based on sound theoretical models or unrelated observations. In particular, we show that if the correlation is determined empirically for two luminosities obtained from fluxes and redshifts, then the method suffers from circularity. In the case where the observed correlation between fluxes in very narrow redshift bins is used as a proxy for the luminosity correlation, we show that one is dealing with a pure tautology with no information on distances and cosmological model. We argue that the problem arises because of the incomplete treatment of the correlation, and we use numerical methods with a joint X-ray and ultraviolet quasar data set to demonstrate this shortcoming.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis

A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron–molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits

Time-dependent electromagnetic drives are fundamental for controlling complex quantum systems, including superconducting Josephson circuits. In these devices, accurate time-dependent Hamiltonian models are imperative for predicting their dynamics and designing high-fidelity quantum operations. Existing numerical methods, such as black-box quantization (BBQ) and energy-participation ratio (EPR), excel at modeling the static Hamiltonians of Josephson circuits. However, these techniques do not fully capture the behavior of driven circuits stimulated by external microwave drives, nor do they include a generalized approach to account for the inevitable noise and dissipation that enter through microwave ports. Here, we introduce numerical techniques that leverage classical microwave simulations, efficiently executable in finite-element solvers, to obtain the time-dependent Hamiltonian of microwave-driven superconducting circuits with arbitrary geometries under charge, flux, or mixed electromagnetic modulation. Importantly, our techniques do not rely on a lumped-element description of the superconducting circuit, in contrast to previous approaches to tackling this problem. We demonstrate the versatility of our approach by characterizing the driven properties of realistic circuit devices in complex electromagnetic environments, including coherent dynamics due to charge and flux modulation, as well as drive-induced relaxation and dephasing. Our techniques offer a powerful toolbox for optimizing circuit designs and advancing practical applications in superconducting quantum computing.

Lu, Yao [Yale U.; Yale U. (main); Fermilab] (ORCID↗
DOE OSTI2024

Modeling of Macroscopic Dynamics in Three-Dimensional Plasma Configurations (Final Technical Report)

A numerical simulation-based study to investigate the stability properties of inherently three-dimensional plasma magnetic configurations is presented. These configurations, called stellarators and heliotrons, use external helical coils to provide the twisting magnetic field that is required to confine ionized plasma particles. In contrast to the tokamak configuration, which nominally has the property of axisymmetry, electrical current does not need to be induced in stellarator and heliotron plasma. Experiments have shown that these three-dimensional configurations are remarkably robust to macroscopic instability, even when driven to relatively high levels of plasma pressure. Our understanding of how the plasma is able to withstand macroscopic instability will be enhanced by the work proposed here. The effort will generalize existing numerical modeling capability, and it will apply the new capability to model macroscopic dynamics in these three-dimensional configurations. The development work has been applied to the NIMROD simulation code (https://nimrodteam.org) that was originally based on axisymmetric problem domains. It has been generalized to accommodate the three-dimensional shaping of the plasma volume in stellarators and heliotrons. Its use of equilibrium data has also been generalized, and the implementation allows different numerical representation of the magnetic field. Analysis has been performed to inform the selection of numerical methods, and a method to accelerate the iterative solution of the necessary algebraic systems has been developed and implemented. Verification of the new NIMSTELL code on benchmark problems has also been an important part of the effort.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Numerical approach of the quantum circuit theory

In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Analysis of Nonclassical Fracture Problems for Prestressed Bodies with Interacting Cracks

We consider two types of nonclassical fracture mechanisms, namely, the fracture of cracked bodies with initial (residual) stresses acting along the crack planes and the fracture of solids under compression along parallel cracks. To investigate nonaxisymmetric and axisymmetric problems for infinite solids containing two parallel coaxial cracks or a periodic set of coaxial parallel cracks, we use a combined analytic-numerical method within the framework of the three-dimensional linearized mechanics of solids. The analysis involves the representation of stresses and displacements in the linearized theory via harmonic potential functions. With the use of the integral Fourier–Hankel transformations, the problems are reduced to the solution of Fredholm integral equations of the second kind. This approach allows us to investigate problems in a unified general form for compressible and noncompressible homogeneous isotropic or transversely isotropic elastic bodies with an arbitrary structure of the elastic potential, and the material specification of the model is carried out only in the stage of numerical analysis of the resolving equations obtained in the general form. The effects of initial stresses on the stress intensity factors are analyzed for highly elastic materials and layered composites (modeled as transversely isotropic elastic bodies). The “resonance-like” effects are revealed when compressive initial stresses reach the values corresponding to the local loss of stability of the material in the vicinity of cracks, which, according to the indicated combined method, allows one to determine the critical (limiting) load parameters under the conditions of compression of the body along the cracks. The conclusions concerning the dependences of the stress intensity factors and critical (limiting) parameters of compression on the geometric parameters of the problems are formulated as well as concerning the dependences on physical and mechanical characteristics of the materials.

42 ENGINEERING↗
DOE OSTI2017

Modeling propellant-based stimulation of a borehole with peridynamics

A non-local formulation of classical continuum mechanics theory known as peridynamics is used to study fracture initiation and growth from a wellbore penetrating the subsurface within the context of propellant-based stimulation. The principal objectives of this work are to analyze the influence of loading conditions on the resulting fracture pattern, to investigate the effect of in-situ stress anisotropy on fracture propagation, and to assess the suitability of peridynamics for modeling complex fracture formation. In peridynamics, the momentum equation from the classical theory of solid mechanics is replaced by a non-local analogue, which results in an integrodifferential conservation equation. A continuum material is discretized with a set of material points that interact with all other points within a specified distance. Interactions between points are governed by bonds that can deform and break depending on loading conditions. The accumulated breakage of bonds gives rise to a picture of complex growth of fractures that is seen as a key advantage in the peridynamic representation of discontinuities. It is shown that the loading rate significantly influences the number and ex- tent of fractures initiated from a borehole. Results show that low loading rates produce fewer but longer fractures, whereas high loading rates produce numerous shorter fractures around the borehole. The numerical method is able to predict fracture growth patterns over a wide range of loading and stress conditions. Our results also show that fracture growth is attenuated with increasing in-situ confining stress, and, in the case of confining stress anisotropy, fracture extensions are largest in the direction perpendicular to the minimum compressive stress. Since the results are in broad qualitative agreement with experimental and numerical studies found in the literature, suggesting that peridynamics can be a powerful tool in the study of complex fracture network formation.

42 ENGINEERING↗
DOE OSTI2023

Simulation of Reverse Osmosis Membrane Compaction Using Material Point Method

Reverse Osmosis (RO) is a promising technology to address the impending water-crisis in the upcoming decades. RO at high salinities and high pressures is challenging due to membrane compaction that changes its porosity and permeability. In this study, we present a simulation methodology for membrane structural mechanics to understand pore size distribution and permeability variations under high pressure. We use the material point method (MPM), that solves the solid mechanics equations in a Lagrangian framework. MPM provides many features that make it well-suited for simulating mesoporous membranes. The Lagrangian framework allows for large deformations, easy integration of constitutive models and direct import of complex geometries as particles. The spatial discretization in our MPM solver is achieved using linear or cubic-spline shape functions while the time integration is carried out using the explicit Euler method. A series of images containing detailed pore structures obtained from X-ray tomography is first converted to a collection of material points. Compressive loads are applied to the top layer of the membrane to simulate the application of pressure. The membrane deformation and pore size distribution before and after load application are reported and compared with the experimental measurements. The presentation discusses the numerical methods used, the performance of the solver on high-performance computing machines, and the results of membrane compact in detail.

compaction↗
DOE OSTI2016

Direct single-shot phase retrieval from the diffraction pattern of separated objects

The non-crystallographic phase problem arises in numerous scientific and technological fields. An important application is coherent diffractive imaging. Recent advances in X-ray free-electron lasers allow capturing of the diffraction pattern from a single nanoparticle before it disintegrates, in so-called ‘diffraction before destruction’ experiments. Presently, the phase is reconstructed by iterative algorithms, imposing a non-convex computational challenge, or by Fourier holography, requiring a well-characterized reference field. Here we present a convex scheme for single-shot phase retrieval for two (or more) sufficiently separated objects, demonstrated in two dimensions. In our approach, the objects serve as unknown references to one another, reducing the phase problem to a solvable set of linear equations. We establish our method numerically and experimentally in the optical domain and demonstrate a proof-of-principle single-shot coherent diffractive imaging using X-ray free-electron lasers pulses. Lastly, our scheme alleviates several limitations of current methods, offering a new pathway towards direct reconstruction of complex objects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

malbacR: A Package for Standardized Implementation of Batch Correction Methods for Omics Data

Mass spectrometry is a powerful tool for identifying and analyzing small molecules, such as metabolites and lipids, in com-plex biological samples. Liquid chromatography and gas chromatography mass spectrometry studies quite commonly in-volve large numbers of samples, which can require significant time for sample preparation and analyses. To accommodate such studies, the samples are commonly split into batches. Inevitably, variations in sample handling, temperature fluctua-tion, imprecise timing, column degradation and other factors result in systematic errors or biases of the measured abundances between the batches. Numerous methods are available via R packages to assist with batch correction for small molecule om-ics data; however, since these methods were developed by different research teams, the algorithms are available in separate R packages, each with different data input and output formats. We introduce the malbacR package which consolidates eleven common batch effect correction methods for small molecule omics data into one place so users can easily implement and compare: pareto scaling, power scaling, range scaling, ComBat, EigenMS, NOMIS, RUV-random, QC-RLSC, WaveI-CA2.0, TIGER, and SERRF. The malbacR package standardizes data input and output formats across these batch correction methods. The package works in conjunction with the pmartR package, allowing users to seamlessly include batch effect cor-rection in a pmartR workflow without needing any additional data manipulation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Function space requirements for the single-electron functions within the multiparticle Schroedinger equation

Our previously described method to approximate the many-electron wavefunction in the multiparticle Schroedinger equation reduces this problem to operations on many single-electron functions. In this work, we analyze these operations to determine which function spaces are appropriate for various intermediate functions in order to bound the output. This knowledge then allows us to choose the function spaces in which to control the error of a numerical method for single-electron functions. We find that an efficient choice is to maintain the single-electron functions in L{sup 2} Intersection L{sup 4}, the product of these functions in L{sup 1} Intersection L{sup 2}, the Poisson kernel applied to the product in L{sup 4}, a function times the Poisson kernel applied to the product in L{sup 2}, and the nuclear potential times a function in L{sup 4/3}. Due to the integral operator formulation, we do not require differentiability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Observing and modeling the effects of production infrastructure in electromagnetic surveys

Electromagnetic (EM) methods are among the original techniques for subsurface characterization in exploration geophysics because of their particular sensitivity to the earth electrical conductivity, a physical property of rocks distinct yet complementary to density, magnetization, and strength. However, this unique ability also makes them sensitive to metallic artifacts — infrastructure such as pipes, cables, and other forms of cultural clutter — the EM footprint of which often far exceeds their diminutive stature when compared to that of bulk rock itself. In the hunt for buried treasure or unexploded ordnance, this is an advantage; in the long-term monitoring of mature oil fields after decades of production, it is quite troublesome indeed. In this study we consider the latter through the lens of an evolving energy industry landscape in which the traditional methods of EM characterization for the exploration geophysicist are applied toward emergent problems in well-casing integrity, carbon capture and storage, and overall situational awareness in the oil field. We introduce case studies from these exemplars, showing how signals from metallic artifacts can dominate those from the target itself and impose significant burdens on the requisite simulation complexity. Furthermore, we show how recent advances in numerical methods mitigate the computational explosivity of infrastructure modeling, providing feasible and real-time analysis tools for the desktop geophysicist. Lastly, we demonstrate through comparison of field data and simulation results that incorporation of infrastructure into the analysis of such geophysical data is, in a growing number of cases, a requisite but now manageable step.

58 GEOSCIENCES↗
DOE OSTI2018

Center for Extended Magnetohydrodynamic Modeling (CEMM), Final Technical Report for UW-Madison Engineering Physics

The Center for Extended Magnetohydrodynamic Modeling (CEMM) focused on the further development, verification, validation, and application of two scientific computation programs, the NIMROD and M3D-C1 codes, for modeling macroscopic dynamics in magnetized plasma. Both NIMROD and M3D-C1 solve the mathematical equations that model two-fluid 3D magnetohydrodynamic (MHD). They are designed and optimized to be efficient and accurate for toroidal confinement physics calculations. The effort improved the fidelity of the physics models, the realism of the treatment of the surrounding vessel, coils, and other structures, the accuracy and efficiency of the algorithms, and the ability to scale calculations to thousands of processors in order to take advantage of leading-edge computers. The primary application areas of Resonant Magnetic Perturbations (RMP), Edge Harmonic Oscillations (EHO), Edge Localized Modes (ELMs), Disruption Studies, Sawteeth and Stationary States, and Kinetic MHD and Neoclassical Tearing Modes (NTM) are of concern for the international ITER experiment, which is under construction in France. The effort by the UW-Madison Engineering Physics component of CEMM improved the numerical methods in the NIMROD code with respect to modeling MHD interchange and two-fluid effects. It also improved the algorithm for solving large algebraic systems to enhance NIMROD's computational performance when running the code in parallel on increasing numbers of processor cores. The modeling efforts included a study of the nonlinear evolution of ballooning, and the findings were supported by analytical theory and computation. Numerical MHD modeling also examined the influences of two-fluid effects on ELMs and RMPs, where "two-fluid" refers to separation of electron dynamics from ion dynamics. Another related aspect considered the effects of a localized layer of electrical current density near the edge of the plasma confinement region. Two-fluid effects on resonant reconnecting instabilities were verified and applied to computations of sawtooth and drift-tearing dynamics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Systematic Quantum Cluster Typical Medium Method for the Study of Localization in Strongly Disordered Electronic Systems

Great progress has been made in recent years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of disorder and electron-electronic interactions on equal footing. They include dynamical mean-field theory and the Coherent Potential Approximation, and their cluster extension, the dynamical cluster approximation. Despite their successes, these methods do not enable the first-principles study of the strongly disordered regime, including the effects of electronic localization. The main focus of this review is the recently developed typical medium dynamical cluster approximation for disordered electronic systems. This method has been constructed to capture disorder-induced localization and is based on a mapping of a lattice onto a quantum cluster embedded in an effective typical medium, which is determined self-consistently. Unlike the average effective medium-based methods mentioned above, typical medium-based methods properly capture the states localized by disorder. The typical medium dynamical cluster approximation not only provides the proper order parameter for Anderson localized states, but it can also incorporate the full complexity of Density-Functional Theory (DFT)-derived potentials into the analysis, including the effect of multiple bands, non-local disorder, and electron-electron interactions. After a brief historical review of other numerical methods for disordered systems, we discuss coarse-graining as a unifying principle for the development of translationally invariant quantum cluster methods. Together, the Coherent Potential Approximation, the Dynamical Mean-Field Theory and the Dynamical Cluster Approximation may be viewed as a single class of approximations with a much-needed small parameter of the inverse cluster size which may be used to control the approximation. We then present an overview of various recent applications of the typical medium dynamical cluster approximation to a variety of models and systems, including single and multiband Anderson model, and models with local and off-diagonal disorder. We then present the application of the method to realistic systems in the framework of the DFT and demonstrate that the resulting method can provide a systematic first-principles method validated by experiment and capable of making experimentally relevant predictions. We also discuss the application of the typical medium dynamical cluster approximation to systems with disorder and electron-electron interactions. Most significantly, we show that in the limits of strong disorder and weak interactions treated perturbatively, that the phenomena of 3D localization, including a mobility edge, remains intact. However, the metal-insulator transition is pushed to larger disorder values by the local interactions. We also study the limits of strong disorder and strong interactions capable of producing moment formation and screening, with a non-perturbative local approximation. Here, we find that the Anderson localization quantum phase transition is accompanied by a quantum-critical fan in the energy-disorder phase diagram.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Large Eddy Simulation of Autoignition Transients in a Model Diesel Injector Configuration

Developing an improved understanding of transient mixing and combustion processes inherent in diesel injection is an important element in the design of advanced engines. This paper provides a detailed analysis of these processes using an idealized benchmark configuration designed to facilitate precise comparisons between different models and numerical methods. The computational domain is similar to the Engine Combustion Network (www.sandia.gov/ECN) Spray-A injector with n-dodecane as the fuel. Quantified idealizations are made in the treatment of boundary conditions to eliminate ambiguities and unknowns associated with the actual injector(s) used in the experiment. These ambiguities hinder comparisons aimed at understanding the accuracy of different models and the coupled effects of potential numerical errors. Prior to understanding the impact of injector imperfections on their performance, it is first necessary to understand how models perform in a well-controlled environment with well-defined boundary conditions. Here, we focus on the latter while accurately matching the operating conditions used in the experiments. Relevant high-pressure phenomena are treated with real-fluid thermodynamics and transport for multicomponent mixtures. A highly resolved calculation is performed to study both scalar-mixing and initiation of combustion. Results are assembled into a database that can facilitate one-to-one comparisons between codes. The combined set of results is analyzed to provide physical insights related to localized broadband transient mixing and combustion processes that are typically not available from experiments.

Hakim, Layal↗