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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

An extension of the localized artificial diffusivity method for immiscible and high density ratio flows

The localized artificial diffusivity (LAD) method is widely regarded as the preferred multi-material regularization scheme for the compact finite difference method, because it is conservative, easy to implement, and generally robust for a wide range of multi-material problems. However, traditional LAD methods face significant challenges when applied to flows with large density ratios and when maintaining thermodynamic equilibrium across material interfaces. These limitations arise from the formulation of the artificial diffusivity flux and the reliance on enthalpy diffusion for interface regularization. Additionally, traditional LAD methods struggle to ensure stability under large density ratio conditions, fail to maintain a finite interface thickness, and are therefore unsuitable for modeling immiscible interfaces. Here, in this work, we discuss the origins of these issues in traditional LAD methods and propose modifications which enable the simulation of large density ratio and immiscible flows. The proposed method targets the artificial diffusion fluxes at gradients and ringing in the volume fraction, rather than the mass fraction in traditional methods, to consistently regularize large density ratio interfaces. Furthermore, the proposed method introduces an artificial bulk density diffusion term to enforce equilibrium conditions across interfaces. To address the challenge of modeling immiscible flows, a conservative diffuse interface term is incorporated into the formulation to ensure a finite interface thickness. Specific consideration is taken in the design of the method to ensure that these crucial properties are maintained for N -material flows. The effectiveness of the proposed method is demonstrated through a series of canonical test cases, and its accuracy is validated by comparison with experimental data on micro-bubble collapse in water. These results highlight the method’s robustness and its ability to overcome the limitations of traditional LAD approaches.

Artificial diffusivity↗
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↗
DOE OSTI2019

A Finite-Element Approach for the Partitioning of Carbon in Q&P Steel

This paper reports a Galerkin finite-element analysis of carbon partitioning from martensite into austenite during the quenching and partitioning (Q&P) processes in steels. In contrast to classical or sophisticated diffusion field models, an alternative nonlinear governing equation based on chemical potential and composition is considered. The model is applied to simulate the carbon partitioning of modified 22MnB5 alloys assuming an immobile austenite–martensite phase boundary and, in turn, is compared with experimental measurements of the volume fraction and carbon content of retained austenite. The simulations show outstanding results on the influence of Si and C content on the partitioning parameters.

36 MATERIALS SCIENCE↗
DOE OSTI2015

The effects of phase decorrelation on the dynamics of the bump-on-tail instability

The dynamics of the bump-on-tail instability has been studied. The novelty of the work is the analysis of how the bump-on-tail dynamics is affected by an extrinsic stochastisation of the phase of the wave-particle interaction; here referred to as phase decorrelation. For this purpose, a nonlinear Monte Carlo model has been developed. When the characteristic time scale for macroscopic phase decorrelation becomes shorter than time scales of nonlinear wave-particle dynamics, the system may be described quasilinearly, with the phase decorrelation being replaced by a quasilinear diffusion coefficient in particle energy. A purely quasilinear Monte Carlo model, which is typically less computationally demanding than the fully nonlinear description due to the reduced dimensionality of phase space, has been developed for comparison. In this paper, parameter regimes, where the nonlinear and the quasilinear descriptions quantitatively agree on a macroscopic level, have been investigated, using combined theoretical and numerical analyses. Qualitative effects on the macroscopic dynamics by the presence of phase decorrelation and/or by structures of the energy distribution function in the proximity of the wave-particle resonance are also studied.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Velocity space evolution of a minority energetic electron population undergoing the anomalous Doppler instability

The kinetic evolution in velocity space of a minority suprathermal electron population that is undergoing the anomalous Doppler instability (ADI) is investigated using the results from fully nonlinear numerical simulations that self-consistently evolve particles and fields in a plasma. Electron trajectories in phase space during different stages of the ADI are captured, and are analysed in relation to the characteristics of the excited electric fields and of the overall distribution of particles. For some electrons, trapping and mirroring effects are observed during the saturation phase. A relationship between the second order moments of the perpendicular electron distribution function and time is established, and is used to investigate the range of applicability of analytical approximations drawn from classical theory, that involve a quasilinear wave-driven diffusion operator.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

COSMIC-RAY PITCH-ANGLE SCATTERING IN IMBALANCED MHD TURBULENCE SIMULATIONS

Pitch-angle scattering rates for cosmic-ray particles in MHD simulations with imbalanced turbulence are calculated for fully evolving electromagnetic turbulence. We compare with theoretical predictions derived from the quasilinear theory of cosmic-ray diffusion for an idealized slab spectrum and demonstrate how cross helicity affects the shape of the pitch-angle diffusion coefficient. Additional simulations in evolving magnetic fields or static field configurations provide evidence that the scattering anisotropy in imbalanced turbulence is not primarily due to coherence with propagating Alfvén waves, but an effect of the spatial structure of electric fields in cross-helical MHD turbulence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Modulating effect of evanescent waves on thin film growth

Atomic-scale smooth thin films are keys to successful integration and proper function of many multilayer-structured devices. However, the intrinsic islandlike growth mode prevents human beings from realizing such ultrasmooth films of many important functional materials. To solve this problem, we propose a negative entropy-infusing method that employs evanescent waves to enhance the downward interlayer diffusion of adatoms and thus transform the islandlike growth mode to the layer-by-layer growth mode. In this work, the formulas of the optical force and the lowered diffusion barrier were derived, and the application of this theory on a simplified example demonstrates significantly improved surface morphologies through numerical simulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Random Walks With Tweedie: A Unified View of Score-Based Diffusion Models [In the Spotlight]

We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals—particularly natural images—and often play a role in state-of-the-art algorithms for inverse problems in image processing. While these algorithms are often surprisingly simple, the theory behind them is not, and multiple complex theoretical justifications exist in the literature. Here, in this study, we provide a simple and largely self-contained theoretical justification for score-based diffusion models that is targeted towards the signal processing community. This approach leads to generic algorithmic templates for training and generating samples with diffusion models. We show that several influential diffusion models correspond to particular choices within these templates and demonstrate that alternative, more straightforward algorithmic choices can provide comparable results. This approach has the added benefit of enabling conditional sampling without any likelihood approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Grazing-incidence X-ray diffraction from a crystal with subsurface defects

The diffraction of X rays incident on a crystal surface under grazing angles under conditions of total external reflection has been investigated. An approach is proposed in which exact solutions to the dynamic problem of grazing-incidence diffraction in an ideal crystal are used as initial functions to calculate the diffuse component of diffraction in a crystal with defects. The diffuse component of diffraction is calculated for a crystal with surface defects of a dilatation-center type. Exact formulas of the continuum theory which take into account the mirror-image forces are used for defect-induced atomic displacements. Scattering intensity maps near Bragg peaks are constructed for different scan modes, and the conditions for detecting primarily the diffuse component are determined. The results of dynamic calculations of grazing-incidence diffraction in defect-containing crystals are compared with calculations in the kinematic approximation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

X-ray diffraction study of BaTiO{sub 3} single crystals before and after fast-neutron irradiation

The neutron irradiation of ferroelectrics is efficiently used to form structural states that cannot be obtained by conventional technologies. To date, the effect of neutron irradiation on the structure and properties of BaTiO{sub 3} has been studied for only ceramic materials. We have considered the influence of fast-neutron irradiation (F = 1 × 10{sup 17} cm{sup −2}) on the structure and properties of BaTiO{sub 3} single crystals for the first time. The structural changes occurring in irradiated BaTiO{sub 3} and their correlation with the behavior of dielectric and nonlinear optical characteristics are analyzed with the aid of a specially developed method for taking into account the experimental correction to diffuse scattering. Neutron irradiation to the aforementioned dose retains the polar structure of the material and only slightly changes atomic displacements. The radiationinduced structural changes occur according to the high-temperature type to form a structure similar to the cubic modification of unirradiated BaTiO{sub 3} crystal.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

LOCAL SIMULATIONS OF INSTABILITIES DRIVEN BY COMPOSITION GRADIENTS IN THE ICM

The distribution of helium in the intracluster medium (ICM) permeating galaxy clusters is not well constrained due to the very high plasma temperature. Therefore, the plasma is often assumed to be homogeneous. A nonuniform helium distribution can, however, lead to biases when measuring key cluster parameters. This has motivated one-dimensional models that evolve the ICM composition assuming that the effects of magnetic fields can be parameterized or ignored. Such models for nonisothermal clusters show that helium can sediment in the cluster core, leading to a peak in concentration offset from the cluster center. The resulting profiles have recently been shown to be linearly unstable when the weakly collisional character of the magnetized plasma is considered. In this paper, we present a modified version of the MHD code Athena, which makes it possible to evolve a weakly collisional plasma subject to a gravitational field and stratified in both temperature and composition. We thoroughly test our implementation and confirm excellent agreement against several analytical results. In order to isolate the effects of composition, in this initial study we focus our attention on isothermal plasmas. We show that plasma instabilities, feeding off gradients in composition, can induce turbulent mixing and saturate by rearranging magnetic field lines and alleviating the composition gradient. Composition profiles that increase with radius lead to instabilities that saturate by driving the average magnetic field inclination to roughly 45°. We speculate that this effect may alleviate the core insulation observed in homogeneous settings, with potential consequences for the associated cooling flow problem.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Turbulent dynamo in a conducting fluid and a partially ionized gas

By following the Kazantsev theory and taking into account both microscopic and turbulent diffusion of magnetic fields, we develop a unified treatment of the kinematic and nonlinear stages of a turbulent dynamo process, and we study the dynamo process for a full range of magnetic Prandtl number P {sub m} and ionization fractions. We find a striking similarity between the dependence of dynamo behavior on P {sub m} in a conducting fluid and R (a function of ionization fraction) in a partially ionized gas. In a weakly ionized medium, the kinematic stage is largely extended, including not only exponential growth but a new regime of dynamo characterized by a linear-in-time growth of magnetic field strength, and the resulting magnetic energy is much higher than the kinetic energy carried by viscous-scale eddies. Unlike the kinematic stage, the subsequent nonlinear stage is unaffected by microscopic diffusion processes and has a universal linear-in-time growth of magnetic energy with the growth rate as a constant fraction 3/38 of the turbulent energy transfer rate, showing good agreement with earlier numerical results. Applying the analysis to the first stars and galaxies, we find that the kinematic stage is able to generate a field strength only an order of magnitude smaller than the final saturation value. But the generation of large-scale magnetic fields can only be accounted for by the relatively inefficient nonlinear stage and requires longer time than the free-fall time. It suggests that magnetic fields may not have played a dynamically important role during the formation of the first stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Determining pitch-angle diffusion coefficients from test particle simulations

The transport and acceleration of charged particles in turbulent media are topics of great interest in space physics and interstellar astrophysics. These processes are dominated by the scattering of particles off magnetic irregularities. The scattering process itself is usually described by small-angle scattering, with the pitch-angle coefficient D{sub μμ} playing a major role. Since the diffusion coefficient D{sub μμ} can be determined analytically only for the approximation of quasilinear theory, the determination of this coefficient from numerical simulations has become more important. So far these simulations have yielded particle tracks for small-scale scattering, which can then be interpreted using the running diffusion coefficients. This method has a limited range of validity. This paper presents two new methods that allow for the calculation of the pitch-angle diffusion coefficient from numerical simulations. These methods no longer analyze particle trajectories and instead examine the change of particle distribution functions. It is shown that these methods provide better resolved results and allow for the analysis of strong turbulence. The application of these methods to Monte Carlo simulations of particle scattering and hybrid MHD-particle simulations is presented. Both analysis methods are able to recover the diffusion coefficients used as input for the Monte Carlo simulations and provide better results in MHD simulations, especially for stronger turbulence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

HEATING OF THE PARTIALLY IONIZED SOLAR CHROMOSPHERE BY WAVES IN MAGNETIC STRUCTURES

In this paper, we show a “proof of concept” of the heating mechanism of the solar chromosphere due to wave dissipation caused by the effects of partial ionization. Numerical modeling of non-linear wave propagation in a magnetic flux tube, embedded in the solar atmosphere, is performed by solving a system of single-fluid quasi-MHD equations, which take into account the ambipolar term from the generalized Ohm’s law. It is shown that perturbations caused by magnetic waves can be effectively dissipated due to ambipolar diffusion. The energy input by this mechanism is continuous and shown to be more efficient than dissipation of static currents, ultimately leading to chromospheric temperature increase in magnetic structures.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A hyperbolic-equation system approach for magnetized electron fluids in quasi-neutral plasmas

A new approach using a hyperbolic-equation system (HES) is proposed to solve for the electron fluids in quasi-neutral plasmas. The HES approach avoids treatments of cross-diffusion terms which cause numerical instabilities in conventional approaches using an elliptic equation (EE). A test calculation reveals that the HES approach can robustly solve problems of strong magnetic confinement by using an upwind method. The computation time of the HES approach is compared with that of the EE approach in terms of the size of the problem and the strength of magnetic confinement. The results indicate that the HES approach can be used to solve problems in a simple structured mesh without increasing computational time compared to the EE approach and that it features fast convergence in conditions of strong magnetic confinement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Modeling of Nonlocal Electron Conduction for Inertial Confinement Fusion

In this report Chenhall presents a new Monte Carlo (MC) transport method developed as part of his PhD thesis work funded via fellowship by Sandia National Laboratories. The model is used to simulate the electron thermal transport within inertial confinement fusion (ICF) type problems. The new model aims to improve upon the currently used implicit Schurtz, Nicolai, and Busquet (iSNB) method, in particular by using finite particle ranges in comparison to the exponential solution of a diffusion method and by improved higher order angular modeling. The new method is being developed using the 1D LILAC and 2D DRACO codes developed by the Rochester Laboratory for Laser Energetics. The model is compared to iSNB for several ICF type problems: Omega shot 60303 a shock timing experiment, Omega shot 68951 a cryo target implosion and a NIF phase plate polar direct drive design. Overall, the MC method performs at least as well as the iSNB method and appears to indicate a lower predicted preheat ahead of the shock fronts. However, the difference in overall results between iSNB and MC transport is small for the choice of test problems and further simulations will need to be run to fully understand the difference between the models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Recent Progress on Numerical Modeling for Microgravity Electric Field Flames: Preprint

This paper presents the recent progress on the NASA Physical Science Informatics (PSI) project PeleLM CFD of Ion Driven Winds from Diffusion Flames in simulating the E-FIELD Flames microgravity results. The focus of this project is to comprehensively simulate the behavior of a small diffusion flame under the influence of an externally applied electric field in zero-gravity. To date, the capability of accurately simulating electric field flames has eluded researchers because the system exhibits dramatic ranges of coupled temporal and spatial scales. Moreover, in earth gravity the hot combustion products are subject to buoyancy effects that are difficult to isolate from those generated by the electric field. This work is an implementation in an existing powerful simulation framework (PeleLM) for this problem using PeleLMeX in order to validate the model and investigate the complex coupled system. The current effort includes establishing the domain of a diffusion coflow burner, examining the boundary conditions, flame geometry and ignition with gravitational forces and also with an electric field applied. A detailed model is used that includes the chemistry of charged ions and chemiluminescent flame intermediates to capture any feedback between ion-driven convection and combustion behavior, and to allow quantitative comparisons with experimental measurements.

coflow flames↗
DOE OSTI2018

Diffusion of Innovations: Interplay of Social, Economic, Technological, and Policy Drivers in the Solar Industry. Summary of UT Austin Student Capstone Research Projects

The University of Texas at Austin’s Policy Research Project (PRP), a nine-month (two semesters) capstone, is a keystone of the core curriculum at the LBJ School of Public Affairs. In PRPs, small groups of students, under the mentorship of a faculty director, take on real-world problems that require special knowledge and skill sets. PRPs expose students to challenges in formulating and executing research, and in communicating academic research and related complex data to broader stakeholder communities and decision makers. The PRP structure is an innovative and effective approach for integrating research within the teaching and training of graduate students who are preparing themselves to address important real-world problems at the intersection of society, economics, technology, and policy. The project summaries below describe seven papers developed during September 2017 – May 2018 as part of a PRP on “Diffusion of Innovations: Interplay of Social, Economic, Technological, and Policy Drivers in the Solar Industry.” Twenty graduate students, drawn from the LBJ School’s Masters in Public Affairs and Masters in Global Policy Studies programs and the Jackson School Geoscience’s Energy and Earth Resources program, participated in this PRP. Dr. Varun Rai, Associate Professor and Associate Dean for Research at the LBJ School, directed the PRP, with support from his research team including: Dr. Ariane Beck, Dr. Ashok Sekar, D. Cale Reeves, and Erik Funkhouser. Clients for the project included the U.S. Department of Energy (Casey Canfield), Lawrence Berkeley National Laboratory (Ben Hoen, Galen Barbose Joachim Seel, Naïm Darghouth, Ryan Wiser), and National Renewable Energy Laboratory (Benjamin Sigrin, Eric O’Shaughnessy). The seven projects separately addressed one of the following topics: (1) low- and middle-income PV adoption, (2) modeling economic and information intervention design, (3) evaluation of DOE’s Solar in Your Community Challenge, (4) property value impacts near large-scale solar facilities, (5) solar market maturity and evolution of business models, (6) social media data for predicting PV adoption, and (7) individual-level variation in adoption of innovations. Many of the papers relied on data collected and curated by Lawrence Berkeley National Laboratory, including data embedded within the annual Tracking the Sun and Utility-Scale Solar reports. Each of the seven teams in the PRP prepared a research paper. The PRP culminated with a full-day conference at UT Austin in May 2018 to present findings from the seven projects in this PRP to a broad audience of about 75 experts from academia, national labs, industry, and government from across the country.

14 SOLAR ENERGY↗