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DOE OSTI2021

Physics-Informed Machine Learning Models for Predicting the Progress of Reactive-Mixing

This paper presents a physics-informed machine learning (ML) framework to construct reduced-order models (ROMs) for reactive-transport quantities of interest (QoIs) based on high-fidelity numerical simu-lations. QoIs include species decay, product yield, and degree of mixing. The ROMs for QoIs are applied to quantify and understand how the chemical species evolve over time. First, high-resolution datasets for constructing ROMs are generated by solving anisotropic reaction-di?usion equations using a non-negative finite element formulation for di?erent input parameters. The reactive-mixing model input parameters are: time-scale associated with flipping of velocity, spatial-scale controlling small/large vortex structures of velocity, perturbation parameter of the vortex-based velocity, anisotropic dispersion strength/contrast, and molecular diffusion. Second, random forests, F-test, and mutual information criterion are used to evaluate the importance of model inputs/features with respect to QoIs. We observed that anisotropic dispersion strength/contrast is the most important feature and time-scale associated with flipping of velocity is the least important feature. Third, Support Vector Machines (SVM) and Support Vector Regression (SVR) are used to construct ROMs based on the model inputs. The constructed SVR-ROMs are then used to predict scaling of QoIs. We also present estimates and inequalities on the QoIs, which inform that the species decay, mix, and produce in an exponential fashion. These inequalities also inform that a radial basis function is the most suitable kernel for the SVM/SVR models for QoIs. It is observed that R2-score for SVR-ROMs on unseen data is greater than 0.9, implying that the SVR-ROMs are able to predict the reaction-diffusion system state reasonably well. Finally, in terms of the computational cost, the proposed SVM-ROMs are O(107) times faster than running a high-fidelity finite element simulation for evaluating QoIs. This makes the proposed ML-based ROMs attractive for reactive-transport sensing and real-time monitoring applications as they are significantly faster yet reasonably accurate.

Mudunuru, Maruti K.↗

DOE OSTI2015

On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

Several computer codes simulating chemical reactions in particles systems are based on the Green's functions of the diffusion equation (GFDE). Indeed, many types of chemical systems have been simulated using the exact GFDE, which has also become the gold standard for validating other theoretical models. In this work, a simulation algorithm is presented to sample the interparticle distance for partially diffusion-controlled reversible ABCD reaction. This algorithm is considered exact for 2-particles systems, is faster than conventional look-up tables and uses only a few kilobytes of memory. The simulation results obtained with this method are compared with those obtained with the independent reaction times (IRT) method. This work is part of our effort in developing models to understand the role of chemical reactions in the radiation effects on cells and tissues and may eventually be included in event-based models of space radiation risks. However, as many reactions are of this type in biological systems, this algorithm might play a pivotal role in future simulation programs not only in radiation chemistry, but also in the simulation of biochemical networks in time and space as well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Features of the dynamics of particles and fields at cyclotron resonances

Some features of the dynamics of particles and fields at cyclotron resonances have been discussed with the focus on chaotic dynamical regimes. It has been shown that the known criterion of the transition of the regular dynamics of particles to chaotic dynamics at cyclotron resonances sometimes describes this transition incorrectly. The reason for such a feature of the criterion has been revealed. The anomalous sensitivity of the dynamics of particles to external fluctuations at autoresonance has been analyzed. A theory of excitation of electromagnetic waves by a beam of phased oscillators under the conditions of isolated nonlinear cyclotron resonance has been developed. It has been shown that the chaotic dynamical regime is due to the periodic change in the structure of the phase portrait of particles in the wave field. It has been shown that higher moments can play a more significant role than lower moments in almost all chaotic dynamical regimes at cyclotron resonances. In this case, the known kinetic diffusion equations should be generalized with the inclusion of these higher moments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Mathematical model of testing of pipeline integrity by thermal fields

Thermal fields testing at the ground surface above a pipeline are considered. One method to obtain and investigate an ideal thermal field in different environments is a direct numerical simulation of heat transfer processes taking into account the most important physical factors. In the paper a mathematical model of heat propagation from an underground source is described with accounting of physical factors such as filtration of water in soil and solar radiation. Thermal processes are considered in 3D origin where the heat source is a pipeline with constant temperature and non-uniform isolated shell (with 'damages'). This problem leads to solution of heat diffusivity equation with nonlinear boundary conditions. Approaches to analysis of thermal fields are considered to detect damages.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2016

Measurement of Kinetic Parameters by Oscillated Experiments

The availability of reliable values of the kinetic parameters (effective delayed neutron fraction {beta} and effective mean neutron generation time {Lambda}) is important for reactor kinetic analyses and for reactivity monitoring when adopting the point kinetic approach. The kinetic parameters may be obtained either by simulations (Monte Carlo or deterministic) of the system or by direct measurements. Several methods have been proposed for the direct experimental determination of the kinetic parameters, e.g. control rod drops and noise analysis approaches, e.g. In this work, the problem of the determination of kinetic parameters in subcritical systems is tackled. The system is subjected to an oscillated source and the value of the ratio {beta}/{Lambda} is related to a measurable quantity when the system response reaches an equilibrium condition. In the analysis presented, a pure frequency is considered: when analyzing more complicated source periodic behaviours, a Fourier analysis can allow to isolate the contributions of individual frequencies. The phase difference between the oscillating source and the system response is adopted as the experimental observable. The method for the interpretation of the measurements is based on the standard point kinetic model. The response of the system is obtained by localized neutron detectors and, therefore, spatial and spectral effects may also affect the results. This drawback needs some further discussion and will be considered in the future work. The phase shift between the source signal and the system response may be analytically retrieved by Laplace transforming the point kinetic equations in the presence of an oscillated source. An explicit formula relates the phase shift to the ratio {beta}/{Lambda} and to the frequency of the source. Based on this relationship, the ratio {beta}/{Lambda} can be determined. To validate the technique, the experimental data are simulated by a numerical code solving the time-dependent diffusion equations for a source-driven system. The work allows to assess the possibility of the technique and its limits of applicability. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1990

Asymptotic analysis of dissipative waves with applications to their numerical simulation

Various problems involving the interplay of asymptotics and numerics in the analysis of wave propagation in dissipative systems are studied. A general approach to the asymptotic analysis of linear, dissipative waves is developed. It was applied to the derivation of asymptotic boundary conditions for numerical solutions on unbounded domains. Applications include the Navier-Stokes equations. Multidimensional traveling wave solutions to reaction-diffusion equations are also considered. A preliminary numerical investigation of a thermo-diffusive model of flame propagation in a channel with heat loss at the walls is presented.

Hagstrom, Thomas↗

DOE OSTI2016

JASMINE: a fuel rod thermal-mechanical performance's code

JASMINE, which is developed by China General Nuclear Power Corporation (CGNPC), is a code for calculating thermal-mechanical response of PWR fuel rods. The code models many physical phenomena, including heat conduction through the fuel and cladding to the coolant, cladding elastic and plastic deformation, fuel elastic deformation, fuel swelling and densification,fuel-cladding mechanical interaction, fission gas release from the fuel, rod internal pressure, cladding oxidation and hydriding. Just as most fuel rod codes, JASMINE, which is a quasi-two dimensional code, includes a thermal module, a mechanical module, a fission gas release (FGR) module, and an internal pressure module. For thermal module, the time dependent thermal conduction equation of axisymmetric cylindrical geometry, Halden's fuel thermal conductivity, thermal conductivity integration method and multi-dimension Newton-Raphson procedure are used; for the mechanical module, generalized plane strain hypothesis, cladding-fuel axial lockup model, cladding thermal stress and transfer matrix method are applied; for fission gas release module, the time dependent diffusion equation for a spherical grain, Speight-Turnbull grain surface boundary condition, and Forsberg-Massih's method are used; for the internal pressure module, the ideal gas state equation is used. The code, which is on validation stage, will be used for fuel rod design of nuclear power plants in China in a near future. So far, the preliminary validation process for pellet centerline temperature and fission gas release, which is based on fuel rod test data in FUMEX-III project, has finished. According to the validation results, JASMINE has the ability to reasonably predicts fuel behavior and performance in-pile. JASMINE has good prediction in fuel temperature, and good prediction on FGR as a whole. However, for FGR in the range 1% to 15%, JASMINE over-predicts FGR; for other range, JASMINE underestimates FGR. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2014

Calibration of a thin metal foil for infrared imaging video bolometer to estimate the spatial variation of thermal diffusivity using a photo-thermal technique

A thin metal foil is used as a broad band radiation absorber for the InfraRed imaging Video Bolometer (IRVB), which is a vital diagnostic for studying three-dimensional radiation structures from high temperature plasmas in the Large Helical Device. The two-dimensional (2D) heat diffusion equation of the foil needs to be solved numerically to estimate the radiation falling on the foil through a pinhole geometry. The thermal, physical, and optical properties of the metal foil are among the inputs to the code besides the spatiotemporal variation of temperature, for reliable estimation of the exhaust power from the plasma illuminating the foil. The foil being very thin and of considerable size, non-uniformities in these properties need to be determined by suitable calibration procedures. The graphite spray used for increasing the surface emissivity also contributes to a change in the thermal properties. This paper discusses the application of the thermographic technique for determining the spatial variation of the effective in-plane thermal diffusivity of the thin metal foil and graphite composite. The paper also discusses the advantages of this technique in the light of limitations and drawbacks presented by other calibration techniques being practiced currently. The technique is initially applied to a material of known thickness and thermal properties for validation and finally to thin foils of gold and platinum both with two different thicknesses. It is observed that the effect of the graphite layer on the estimation of the thermal diffusivity becomes more pronounced for thinner foils and the measured values are approximately 2.5–3 times lower than the literature values. It is also observed that the percentage reduction in thermal diffusivity due to the coating is lower for high thermal diffusivity materials such as gold. This fact may also explain, albeit partially, the higher sensitivity of the platinum foil as compared to gold.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Pair dynamics and the intermolecular nuclear Overhauser effect (NOE) in liquids analysed by simulation and model theories: Application to an ionic liquid

Combining simulation and model theories, this paper analyses the impact of pair dynamics on the intermolecular nuclear Overhauser effect (NOE) in liquids. For the first time, we give a distance resolved NOE. When applied to the ionic liquid 1-ethyl-3-methyl-imidazolium tetrafluoroborate the NOE turns out to be of long-range nature. This behaviour translates to the experimentally measured cross- and longitudinal relaxation rates. We were able to calculate the heteronuclear NOE from simulation data, despite the high computational effort. Model theories are computationally less demanding and cover the complete frequency range of the respective spectral density function, they are usually based on a very simple pair distribution function and the solution of the diffusion equation. In order to model the simulated data sufficiently, these simplifications in structure and dynamics have to be generalised considerably.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Inhomogeneous dopant distribution in III–V nanowires

We present a theoretical study of the dopant spatial distribution in III–V nanowires grown by molecular beam epitaxy. The evolution of the dopant concentration is obtained by solving the non-stationary diffusion equation. Within the model, it is shown why and how the dopant inhomogeneity appears, as observed experimentally in the case of Be doping of GaAs nanowires and in other material systems.

36 MATERIALS SCIENCE↗

DOE OSTI2023

A Simplified Approach Based on Cellular Automata for Describing Direct Reduced Iron Production in Different Reducing Conditions

A quick computation approach based on cellular automata is developed and implemented to describe the reduction of iron ore pellets by a mixture of reducing agents featured by different H 2 /CO ratios. The evolution of oxygen concentration inside the pellet is followed from the beginning to the end of contact between reducing agent and pellet. The variation of thermal state of pellets and gas mixture is computed based on their initial temperature, considering the heat involved and the convective heat exchange between pellet and gas mixture. The use of cellular automata and finite‐difference method to solve the diffusion equation point out the absence of any diffusion coefficient value, allowing to make the model fit the experimental trial, because the problem is that it is not ruled just by diffusion but also by the concentration variation of reducing agent inside the pellet due to porosity increasing during reduction. The updating of the reducing agents concentration implies a sharp decrease of oxygen concentration that the cellular automata model considers. The developed model is able to provide the in‐line control of reduction process and could be used to adjust the chemical concentration and temperature of injected reducing agents.

Metallurgy & Metallurgical Engineering↗

DOE OSTI2022

On heat conduction in an irregular magnetic field. Part 1

Anisotropic heat conduction in a plasma embedded in a magnetic field with irregular, possibly chaotic, field lines is discussed. If the collisional mean free path exceeds the electron gyroradius, the heat conductivity is much larger along the field lines than across them, and this enhances the transport across a domain where good flux surfaces do not exist. Recognising that anisotropic heat conduction may be cast in a variational form, and by constructing increasingly sophisticated trial functions that are based on invariant and almost-invariant structures under the magnetic field-line flow, bounds are derived on this enhancement and on the temperature variation along the magnetic field. In this way, remarkably accurate approximations for the temperature can be rapidly constructed without solving the diffusion equation, even in the small perpendicular-diffusion limit when the solution for the temperature is dominated by the fractal structure the magnetic field lines.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

MEUMAPPS (C++ Version)

Many materials, metal alloys in particular, have features on the on micrometer or nanometer scale that have a large impact on the properties of the material. These features are known as the microstructure of the material. Understanding why and how the microstructure forms in a material is of fundamental scientific interest as well as of significant technological interest. The capability to predict microstructure evolution in a material allows the intentional design of microstructures and hence the intentional design of material properties. The phase-field method is one of the leading methods for predicting microstructure evolution. One of the most significant problems for phase-field models is their computational expense. Even limited phase-field simulations can easily require thousands of CPU core-hours to complete, which significantly limits their use. This code provides both a general framework for creating scalable, GPU-accelerated phase-field model applications as well as several applications themselves. The code is capable of using hundreds of GPUs efficiently, which greatly reduces the time required to perform simulations. The code is written with an emphasis on performance portability, that is the ability for the code to run efficiently on a number of different computing architectures without modification of the source code. The performance portability of this code is primarily enabled through the use of two libraries, Kokkos (performance portable data structures and execution patterns) and heFFTe (performance portable distributed 3D fast Fourier transforms). The code consists of a core library, applications, and tests. The core library includes shared functionality between applications. This includes interfaces with fast Fourier transform (FFT) libraries such as heFFTe, data structures based on Kokkos, file input and output capabilities, and a solver for infinitesimal strain mechanical equilibrium problems. Five applications are included in the code. The flagship application is the MEUMAPPS-SS application, which implements the Kim-Kim-Suzuki phase-field model for precipitation for an arbitrary number of phases and components in a metal alloy. Five simpler applications are also included that solve the Eshelby inclusion problem, Allen-Cahn equation, the coupled Allen-Cahn and diffusion equations, and the Cahn-Hilliard equation. The code includes two applications to solve the Cahn-Hilliard equation, one with constant-step-size first-order time integration and the second with adaptive high-order time integration.

DeWitt, Stephen [Oak Ridge National Lab. (ORNL), O↗

NASA NTRS1973

Differential equation of exospheric lateral transport and its application to terrestrial hydrogen

The differential equation description of exospheric lateral transport of Hodges and Johnson is reformulated to extend its utility to light gases. Accuracy of the revised equation is established by applying it to terrestrial hydrogen. The resulting global distributions for several static exobase models are shown to be essentially the same as those that have been computed by Quessette using an integral equation approach. The present theory is subsequently used to elucidate the effects of nonzero lateral flow, exobase rotation, and diurnal tidal winds on the hydrogen distribution. Finally it is shown that the differential equation of exospheric transport is analogous to a diffusion equation. Hence it is practical to consider exospheric transport as a continuation of thermospheric diffusion, a concept that alleviates the need for an artificial exobase dividing thermosphere and exosphere.

Hodges, R. R., Jr.↗

NASA NTRS1979

Interfacial geometry and D-variation effects in two-phase systems

Numerical solutions of the governing diffusion equation for two-phase concentration dependent diffusion coefficients are examined. Solutions were also calculated for planar, cylindrical, and spherical geometries to compare the effect of interface geometries with those caused by concentration-dependent diffusion coefficients, and two methods of averaging D were considered to determine the best averaging method for different types of D-variations. The effects of interface-location criteria on mass conservation and convergence of interface location, diffusion coefficient variation in the alpha and beta-phases of a two-phase binary alloy system, effect of D(alpha) variation in a cylindrical couple on beta-phase thickness, and geometry and D-variation effects on the degree of homogenization were determined. It is concluded that typical D(alpha)-variations can have a greater influence on the kinetics of interdiffusion than the geometry.

Tenney, D. R.↗

DOE OSTI2021

An efficient reconstruction algorithm for diffusion on triangular grids using the nodal discontinuous Galerkin method

High-energy-density (HED) hydrodynamics studies such as those relevant to inertial confinement fusion and astrophysics require highly disparate densities, temperatures, viscosities, and other diffusion parameters over relatively short spatial scales. This presents a challenge for high-order accurate methods to effectively resolve the hydrodynamics at these scales, particularly in the presence of highly disparate diffusion. A significant volume of engineering and physics applications use an unstructured discontinuous Galerkin (DG) method developed based on the finite element mesh generation and algorithmic framework. This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous. Hence, the diffusive flux is not defined on the interface of elements. The proposed numerical approach reconstructs a smooth solution in a parallelogram that is enclosed by the quadrilateral formed by two adjacent triangle elements. The interface between these two triangles is the diagonal of the enclosed parallelogram. Similar to triangles, the mapping of parallelograms from a physical domain to a reference domain is an affine mapping, which is necessary for an accurate and efficient implementation of the numerical algorithm. Thus, all computations can still be performed on the reference domain, which promotes efficiency in computation and storage. This reconstruction does not make assumptions on choice of polynomial basis. Reconstructed DG algorithms have previously been developed for modal implementations of the convection–diffusion equations. However, to the best of the authors’ knowledge, this is the first practical guideline that has been proposed for applying the reconstructed algorithm on a nodal discontinuous Galerkin method with a focus on accuracy and efficiency. As a result, the algorithm is demonstrated on a number of benchmark cases as well as a challenging substantive problem in HED hydrodynamics with highly disparate diffusion parameters.

Computational efficiency↗

DOE OSTI2021

A comparative study of machine learning models for predicting the state of reactive mixing

Mixing phenomena are important mechanisms controlling flow, species transport, and reaction processes in fluids and porous media. Accurate predictions of reactive mixing are critical for many Earth and environmental science problems such as contaminant fate and remediation, macroalgae growth, and plankton biomass evolution. Here, to investigate the evolution of mixing dynamics under different scenarios (e.g., anisotropy, fluctuating velocity fields), a finite-element-based numerical model was built to solve the fast, irreversible bimolecular reaction-diffusion equations to simulate a range of reactive-mixing scenarios. A total of 2,315 simulations were performed using different sets of model input parameters comprising various spatial scales of vortex structures in the velocity field, time-scales associated with velocity oscillations, the perturbation parameter for the vortex-based velocity, anisotropic dispersion contrast (i.e., ratio of longitudinal-to-transverse dispersion), and molecular diffusion. The outputs comprised concentration profiles of reactants and products. The inputs to and outputs from these simulations were concatenated into feature and label matrices, respectively, to train 20 different machine learning (ML) models intended to emulate system behavior. These 20 ML emulators, based on linear methods, Bayesian methods, ensemble learning methods, and multilayer perceptrons (MLPs), were trained to classify the state of mixing and predict three quantities of interest (QoIs) characterizing species production, decay (i.e., average concentration, square of average concentration), and degree of mixing (i.e., variances of species concentration). Unsurprisingly, linear classifiers and regressors failed to reproduce the QoIs; however, ensemble methods (classifiers and regressors) and the MLP model accurately classified the state of reactive mixing and the QoIs. Among ensemble methods, random forest and decision-tree-based AdaBoost faithfully predicted the QoIs. At run time, trained ML emulators produced results times faster than the finite-element simulations. Due to their low computational expense and high accuracy, ensemble and MLP models are excellent emulators for these numerical simulations and great utilities in uncertainty quantification exercises, which can require 1,000s of forward model runs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Room temperature spin transport in undoped (110) GaAs/AlGaAs quantum wells

We are reporting on our first observation of a micrometer-order electron spin transport in a (110) GaAs/AlGaAs multiple quantum well (QW) at room temperature using a space- and time-resolved Kerr rotation technique. A 37-μm transport was observed within an electron spin lifetime of 1.2 ns at room temperature when using an in-plane electric field of 1.75 kV/cm. The spatio-temporal profiles of electron spins were well reproduced by the spin drift-diffusion equations coupled with the Poisson equation, supporting the validity of the measurement. The results suggest that (110) QWs are useful as a spin transport layer for semiconductor spintronic devices operating at room temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗