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DOE OSTI2022

An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD

The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution methods for MHD are extremely challenging due to disparate time and length scales, strong hyperbolic phenomena, and nonlinearity. Additionally, therefore the development of scalable, implicit MHD algorithms and high-resolution adaptive mesh refinement strategies is of considerable importance. In this work, we develop a high-order stabilized finite-element algorithm for the reduced visco-resistive MHD equations based on the MFEM finite element library (mfem.org). The scheme is fully implicit, solved with the Jacobian-free Newton-Krylov (JFNK) method with a physics-based preconditioning strategy. Our preconditioning strategy is a generalization of the physics-based preconditioning methods in Chacón et al. (2002) to adaptive, stabilized finite elements. Algebraic multigrid methods are used to invert sub-block operators to achieve scalability. A parallel adaptive mesh refinement scheme with dynamic load-balancing is implemented to efficiently resolve the multi-scale spatial features of the system. Our implementation uses the MFEM framework, which provides arbitrary-order polynomials and flexible adaptive conforming and non-conforming meshes capabilities. Results demonstrate the accuracy, efficiency, and scalability of the implicit scheme in the presence of large scale disparity. The potential of the AMR approach is demonstrated on an island coalescence problem in the high Lundquist-number regime (≥ 10 7 ) with the successful resolution of plasmoid instabilities and thin current sheets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Multi-element flow-driven spectral chaos (ME-FSC) method for uncertainty quantification of dynamical systems

The flow-driven spectral chaos (FSC) is a recently developed method for tracking and quantifying uncertainties in the long-time response of stochastic dynamical systems using the spectral approach. The method uses a novel concept called enriched stochastic flow maps as a means to construct an evolving finite-dimensional random function space that is both accurate and computationally efficient in time. In this paper, we present a multi-element version of the FSC method (the ME-FSC method for short) to tackle (mainly) those dynamical systems that are inherently discontinuous over the probability space. In ME-FSC, the random domain is partitioned into several elements, and then the problem is solved separately on each random element using the FSC method. Subsequently, results are aggregated to compute the probability moments of interest using the law of total probability. To demonstrate the effectiveness of the ME-FSC method in dealing with discontinuities and long-time integration of stochastic dynamical systems, four representative numerical examples are presented in this paper, including the Van-der-Pol oscillator problem and the Kraichnan-Orszag three-mode problem. Results show that the ME-FSC method is capable of solving problems that have strong nonlinear dependencies over the probability space, both reliably and at low computational cost.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

A face-upwinded spectral element method

Here we present a new high-order accurate discretisation on unstructured meshes of quadrilateral elements. Our Face Upwinded Spectral Element (FUSE) method uses the same node distribution as a high-order continuous Galerkin (CG) method, but with a particular choice of node locations within each element and an upwinded stencil on the face nodes. This results in a number of benefits, including fewer degrees of freedom and straight-forward integration with CG. We present the derivation of the scheme and the analysis of its properties, in particular showing stability using von Neumann analysis. We show numerical evidence for its accuracy and efficiency on multiple classes of problems including convection-dominated flows, Poisson's equation, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A method for bounding high-order finite element functions: Applications to mesh validity and bounds-preserving limiters

We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be used to locally bound any combination of these basis functions. This approach can be applied to any element/basis type at any approximation order, can provide local (i.e., subcell) extremum bounds to a desired level of accuracy, and can be evaluated efficiently on-the-fly in simulations. Furthermore, we show that this approach generally yields more accurate bounds in comparison to traditional methods based on convex hull properties (e.g., Bernstein polynomials). Furthermore, the efficacy of this technique is shown in applications such as mesh validity checks and optimization for high-order curved meshes, where positivity of the element Jacobian determinant can be ensured throughout the entire element, and continuously bounds-preserving limiters for hyperbolic systems, which can enforce maximum principle bounds across the entire solution polynomial.

Bounding box↗

DOE OSTI2018

A discrete element method representation of an anisotropic elastic continuum

A method for modeling cubically anisotropic elasticity within the discrete element method is presented. The discrete element method (DEM) is an approach originally intended for modeling granular materials (sand, soil, and powders); however, recent developments have usefully extended it to model stochastic mechanical processes in monolithic solids which, to date, have been assumed to be elastically isotropic. The method presented here for efficiently capturing cubic elasticity in DEM is an important prerequisite for further extending DEM to capture the influence of elastic anisotropy on the mechanical response of polycrystals, composites, etc. The system demonstrated here uses a directionally assigned stiffness in the bonds between adjacent elements and includes separate schemes for achieving anisotropy with Zener ratios greater and smaller than one. Finally, the model framework is presented along with an analysis of the accessible space of elastic properties that can be modeled and an artificial neural network interpolation scheme for mapping input parameters to model elastic behavior.

42 ENGINEERING↗

DOE OSTI2017

Insight into γ-Ni/γ'-Ni 3 Al interfacial energy affected by alloying elements

Interfacial energy (σ γ/γ' ) of the γ-Ni/γ'-Ni 3 Al interface is critical to understand and design Ni-based superalloys. Here, in the present work, a first-principles methodology with constrained relaxations has been used to study the effect of dilute alloying element (X) on σ γ/γ' of the (100) coherent interface, where the sixteen X's include Al, Co, Cr, Fe, Hf, Mo, Nb, Pd, Pt, Re, Ru, Ta, Ti, W, Y, and Zr. σ γ/γ' = 19 mJ/m 2 has been predicted for the unalloyed γ/γ' interface, agreeing well with the previous estimations. It is found that the σ γ/γ' value is the lowest when alloying element is in γ-Ni, while the addition to γ'-Ni 3 Al increases σ γ/γ' due mainly to the in-plane lattice expansion. Specifically, our calculations show that alloying elements Mo, W, and Re have the largest effect on the σ γ/γ' value by decreasing it to 4–5 mJ/m 2 when partitioned to γ-Ni; Ru and Pt are shown to increase greatly the σ γ/γ' value up to 25–28 mJ/m 2 when partitioned to γ-Ni; all ternary additions substituting for Ni in γ'-Ni 3 Al increase σ γ/γ' except for Pt; and for Ti and Ta, which segregate strongly to γ'-Ni 3 Al and substitute for Al, the σ γ/γ' values increase to 32 and 35 mJ/m 2 , respectively.

36 MATERIALS SCIENCE↗

DOE OSTI2014

Acceleration of matrix element computations for precision measurements

The matrix element technique provides a superior statistical sensitivity for precision measurements of important parameters at hadron colliders, such as the mass of the top quark or the cross-section for the production of Higgs bosons. The main practical limitation of the technique is its high computational demand. Using the example of the top quark mass, we present two approaches to reduce the computation time of the technique by a factor of 90. First, we utilize low-discrepancy sequences for numerical Monte Carlo integration in conjunction with a dedicated estimator of numerical uncertainty, a novelty in the context of the matrix element technique. We then utilize a new approach that factorizes the overall jet energy scale from the matrix element computation, a novelty in the context of top quark mass measurements. The utilization of low-discrepancy sequences is of particular general interest, as it is universally applicable to Monte Carlo integration, and independent of the computing environment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

Finite Element Based Stress Analysis of Graphite Component in High Temperature Gas Cooled Reactor Core Using Linear and Nonlinear Irradiation Creep Models

Irradiation creep plays a major role in the structural integrity of the graphite components in high temperature gas cooled reactors. Finite element procedures combined with a suitable irradiation creep model can be used to simulate the time-integrated structural integrity of complex shapes, such as the reactor core graphite reflector and fuel bricks. In the present work a comparative study was undertaken to understand the effect of linear and nonlinear irradiation creep on results of finite element based stress analysis. Numerical results were generated through finite element simulations of a typical graphite reflector.

High temperature gas cooled reactor, Finite elemen↗

DOE OSTI2020

CU-BENs: A structural modeling finite element library

The present work discusses capabilities within the finite element library CU-BENs. CU-BENs focuses on applying the finite element method to structural mechanics problems encountered within the context of inverse problems and partitioned fluid–structure interaction; thus element formulations are primarily of a structural type — truss, frame, and triangular discrete Kirchhoff theory shells. CU-BENs defaults to the skyline sparse storage scheme for the system matrix, but also supports other storage schemes when using external libraries such as LAPACK and UMFPACK. CU-BENs includes built-in nonlinear solution strategies, such as the Newton Raphson method and modified spherical arc length method, that are available within static analyses as well within the context of transient dynamic analyses involving a generalized-α implementation of the Newmark implicit time integration scheme.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

Liquid Sampling-Atmospheric Pressure Glow Discharge Ionization Source for Elemental Mass Spectrometry

A new, low power ionization source for elemental MS analysis of aqueous solutions is described. The liquid sampling-atmospheric pressure glow discharge (LSAPGD) operates by a process wherein the surface of the liquid emanating from a 75 μm i.d. glass capillary acts as the cathode of the direct current glow discharge. Analytecontaining solutions at a flow rate of 100 μL min-1 are vaporized by the passage of current, yielding gas phase solutes that are subsequently ionized in the < 5 W (maximum of 60 mA and 500 V), ~1 mm3 volume, plasma. The LS-APGD is mounted in place of the normal electrospray ionization source of a Thermo Scientific Exactive orbitrap mass spectrometer system. Basic operating characteristics are described, including the role of discharge power on mass spectral composition, the ability to obtain ultra-high resolution elemental isotopic patterns, and preliminary limits of detection attainable based on the injection of aliquots of multielement standards. While much optimization remains, it is believed that the LS-APGD may present a practical alternative to high-powered (>1 kW) plasma sources typically employed in elemental mass spectrometry, particularly for those cases where costs, operational overhead, and simplicity considerations are important.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Enhancing the Quantification of Critical Elements in WTE and Coal Ash via Alkaline Fusion: Superiority of Lithium Metaborate (LiBO 2 )

Ashes generated from coal combustion, as well as waste incineration, can be a potential source of critical elements necessary for the ongoing transition towards electrification and greener energy technologies. For the quantification of critical elements, traditional methods such as acid digestion are time-intensive and can fail to dissolve critical elements in refractory minerals. One potential solution is to adopt alkaline fusion for faster, total digestion. However, the role of flux choice and the subsequent digestion efficiency (DE) is unknown. Here, we report a systematic investigation on the feasibility of alkaline fusion with Lithium Metaborate (LiBO 2 ) and Lithium Tetraborate (Li 2 B 4 O 7 ) as fluxes for the digestion of two standard reference materials (BCR 176R and SRM 1633c). Our findings suggest that LiBO 2 yields higher DE values than Li 2 B 4 O 7 for several critical REEs and volatiles, such as Pb and Cd. Specifically, for REEs in SRM 1633c, the DE values with LiBO 2 are, on average, ~16 percent higher than those with Li 2 B 4 O 7 . Similarly, for Pb and Cd in BCR 176R, the DE values with LiBO 2 are ~20 percent higher than with Li 2 B 4 O 7 . These results suggest that LiBO 2 is a superior flux for rapid ash digestion.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2026

Role of Elemental Substitution on Hydrogen Incorporation in Characteristic Ti/Fe-Based Oxides

Elemental substitution is well-known to benefit hydrogen storage in the intermetallic compound TiFe; however, the impact of these substituents on the native and passivating surface oxide has not been well-established. Here, we perform density functional theory calculations on several characteristic oxides that are likely to form on exposed TiFe surfaces, specifically, TiO 2 , FeO, TiFeO 3 , and Ti 4 Fe 2 O. In TiO 2 and TiFeO 3 , additional acceptor species substituting for Ti can increase the solubility of protonic hydrogen (H i + ), likely enhancing hydrogen permeation of the oxide layer. In FeO, few dopants will act as acceptors, and hydrogen will incorporate as substitutional H O + , which is likely to be less mobile and will hinder hydrogen permeation. Finally, we find that Ti 4 Fe 2 O, which is thermodynamically metastable, may be stabilized by defects under O-poor conditions, although the presence of certain substitutional elements can destabilize it. In general, Mn, V, and Cr are among the best substituents for enhancing hydrogenation through the oxide layer. In conclusion, our results help to explain what features make additional elements particularly effective for enabling reversible hydrogen storage in TiFe, and they can guide further technological development of high-performing TiFe-based alloys for future energy applications.

organic↗

DOE OSTI2021

Loss and Isotopic Fractionation of Alkali Elements during Diffusion-Limited Evaporation from Molten Silicate: Theory and Experiments

Moderately volatile elements (MVEs) are variably depleted in planetary bodies, reflecting the imprints of nebular and planetary processes. Among MVEs, Na, K, and Rb are excellent tracers for unraveling the history of MVE depletion in planetary bodies because they have similar geochemical behaviors but can be chemically fractionated by evaporation and condensation processes. Furthermore, K and Rb are amenable to high-precision isotopic analyses, which can help constrain the conditions of evaporation and condensation. To quantitatively understand why Na, K, and Rb are depleted in planetary bodies, we have carried out vacuum evaporation experiments from basaltic melt at 1200 and 1400 °C to study their evaporation kinetics and isotopic fractionations. We chose this composition because it is relevant to evaporation from small differentiated planetesimals. The Rb isotopic compositions of the evaporation residues were measured by multicollector inductively coupled plasma mass spectrometry (MC-ICPMS), and the K isotopic compositions were measured along profiles across the residues by secondary ion mass spectrometry (SIMS). In the 1400 °C run products, we found that the concentrations of both K and Rb in the run products decreased from core to rim, which was accompanied by a heavy K isotope enrichment near the surface. This indicates that, in this run, evaporation was limited by diffusion. To use those data quantitatively, we derive analytical equations that describe the evaporation rate and isotopic fractionation associated with diffusion-limited evaporation from a sphere, slab, and cylinder in transient and quasi-steady state regimes. This model is used to tease out the roles that diffusive transport in the melt and evaporation at the melt/gas interface play in setting the elemental depletion and isotopic composition of the residue. Under our experimental conditions, volatility decreases in the order of Na, Rb, and K. Using our experimental results in a thermodynamic model, we have estimated the product γΓ of activity coefficients × evaporation coefficients of Na, Rb, and K. The measured isotopic compositions of the residues are well explained using Rayleigh distillations, whereby the relative volatilities of K and Rb isotopes are given by the square root of their masses. We use our results and previously published data to predict how K and Rb could have been lost as a function of temperature, melt composition, oxygen fugacity, and saturation degree relevant to Vesta’s building blocks. We find that the K and Rb depletions, K/Rb elemental fractionation, and δ 41 K and δ 87 Rb isotopic fractionations of Vesta (as sampled by howardite-eucrite-diogenite (HED) meteorites) are best explained by evaporation of submillimeter size objects for 0.1-10 years at moderate temperatures (~1050 °C) in a medium ~98.8% saturated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

CMPO-Functionalized Silica Sorbents for pH-Tunable Separation and Enrichment of Rare-Earth Elements from Environmental Matrices

Rare-earth elements (REEs) are crucial in many applications, yet mutual separation is challenging due to their similar chemical behavior. Octylphenyl- N,N-diisobutyl carbamoyl methyl phosphine oxide (CMPO) is an organophosphorus ligand originally developed for extracting actinides and lanthanides from spent nuclear fuel. Here, we report a pH-tunable CMPOfunctionalized silica sorbent for selective REE separation from complex aqueous matrices. A CMPO-associated silica gel sorbent was synthesized and characterized by Brunauer−Emmett−Teller (BET) surface area, scanning electron microscopy, and X-ray photoelectron spectroscopy to confirm the surface functionalization and binding behavior. Sorbent performance was evaluated by using a synthetic 46- element solution and a real phosphate rock fertilizer leachate. Notably, REEs were successfully eluted with ultrapure water, demonstrating reversible desorption controlled by pH adjustment. Packed-bed column studies increased the REE mass fraction from 3.6% to 64% (20-fold enrichment), with up to 30-fold enrichment of neodymium. The adsorption process follows the Langmuir isotherm behavior and follows pseudo-second-order kinetics. The uptake capacity of 1 μmol of REEs per 4.2 μmol of CMPO supports the formation of a predominantly 4:1 ligand:rare earth element(III) pseudocomplex. These results demonstrate CMPO-functionalized silica as a selective, water-elutable, and low-chemical-input platform for sustainable REE recovery from environmental and industrial sources.

chelating ligands↗

DOE OSTI2025

Derivation and verification of the direct-sampling method for simulating Monte Carlo flight paths in tetrahedral meshes with linear finite-element cross sections

This paper provides a derivation of a direct-sampling approach for modeling continuously varying cross sections in tetrahedral-mesh-based Monte Carlo codes. Specifically, cross sections are spatially approximated using linear nodal finite elements. A linearization strategy is provided for non-linearly varying cross sections. The method is verified against seven analytical pure-absorber test problems. These test problems also highlight the benefit of using linear finite elements over element-wise-constant cross sections.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2011

Influence of magnetostatic interactions on the magnetization reversal of patterned magnetic elements

The magnetization reversal in patterned thin-film arrays of elliptical submicron permalloy elements has been investigated by magnetic-force microscopy and micro-magneto-optic Kerr effect. Three different spatial arrangements of chains are considered, namely chains aligned parallel to the long axis of the ellipse, chains aligned parallel to the short axis of the ellipse, and arrays with roughly equal element-to-element spacings in both directions. Comparison of the hysteresis loops in an in-plane field perpendicular to the ellipses' long axes shows that the magnetization reversibility is highest for chains along the long axis. This is due to the nearly coherent magnetization rotation in the applied magnetic field and to the formation of a head-to-tail domain arrangement. Other arrangements, such as chains of ellipses aligned parallel to short axis, yield flux-closure domains as the applied magnetic field is changed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2011

Challenges for a reliable shell model description of the neutrinoless double beta decay matrix elements

Assuming that the neutrinos are Majorana particles and the neutrinoless double beta (0{nu}{beta}{beta}) decay is observed, a reliable 0{nu}{beta}{beta} matrix element is necessary to decide the neutrino mass hierarchy and the minimum neutrino mass. Many nuclear structure techniques, including the shell model, are presently used to calculate these matrix elements. In the last few years one could see a slow convergence of these results, but not yet at a level of 20 several shell model effective interactions and varying other parameters, finding results in a range that spans about 20In this contribution we describe challenges for obtaining reliable shell model 0{nu}{beta}{beta} matrix elements, with emphasis to {sup 76}Ge and {sup 82}Se decays.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2011

Uncertainties in nuclear transition matrix elements for neutrinoless {beta}{beta} decay

Uncertainties in nuclear transition matrix elements M{sup (0{nu})} and M{sub N}{sup (0{nu})} due to the exchange of light and heavy Majorana neutrinos, respectively have been estimated by calculating sets of twelve nuclear transition matrix elements for the neutrinoless {beta}{beta} decay of {sup 94,96}Zr, {sup 98,100}Mo, {sup 104}Ru, {sup 110}Pd, {sup 128,130}Te and {sup 150}Nd isotopes in the case of 0{sup +}{yields}0{sup +} transition by considering four different parameterizations of a Hamiltonian with pairing plus multipolar effective two-body interaction and three different parameterizations of Jastrow short range correlations. Exclusion of nuclear transition matrix elements calculated with the Miller-Spencer parametrization reduces the uncertainties by 10%-15%.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗