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At least 19 records

Regression Analysis with the Directed Infusion of Data

Integrating artificial intelligence and machine learning tools into industry necessitates large-scale collaborative efforts that ensure the robust and accurate execution of downstream analytics such as time series prediction, uncertainty quantification, grid optimization, and condition monitoring. However, concerns related to data privacy pervade the nuclear industry due to the proprietary nature of its data and the possibility of data leakage. Legacy techniques such as encryption often require the explicit transmission of data to trustworthy parties, thereby inviting data leakage concerns. The ideal collaboration scenario avoids the explicit dissemination of data/code while maintaining experimental fidelity, which is currently accomplished using various techniques such as trusted execution environments, homomorphic encryption, differential privacy, and multimatrix masking. These techniques, however, often necessitate a trade-off between trust, efficiency, and utility. This article extends a previously proposed technique called the directed infusion of data (DIOD) that ensures data privacy, allows for scalable obfuscation, and combats the risk of data leakage without compromising utility. The experiments discussed in this article examine a regression-type scenario using DIOD with the goal of preserving the inferential link between two variables. Using the point-kinetics equations, regression experiments compare the performance of a model trained using the original data to that of a model trained using the obfuscated data, which produced identical results. Our claim is further strengthened by an information theoretic proof and experiment, which showed that the inferential content between variables remains the same after obfuscation, thereby avoiding the required communication of the proprietary data.

47 - OTHER INSTRUMENTATION

Nuclear Thermal Rocket Emulator for a Hardware-in-the-Loop Test Bed

To support NASA’s mission to use nuclear thermal rockets for future Mars missions, an instrumentation and control test bed has been built at Oak Ridge National Laboratory. The system is designed as a hardware-in-the-loop test bed for testing control elements and autonomous control algorithms for nuclear thermal propulsion rockets. The mock reactor system consists of a modular and scalable framework, using inexpensive components and open-source software. The hardware system consists of a two-phase flow loop and a mock reactor with six control drums. A single-board computer (NVIDIA Jetson) handles reactor core emulation and hosts a message queuing telemetry transport broker that allows user-deployed control algorithms to interact with the system hardware. The reactor emulator receives sensor data from the hardware and provides the simulated performance of the reactor under steady-state, transient, and fault conditions. The emulator uses a reactivity lookup table and the point kinetics equations to solve for the reactor dynamics in real time. Emulated reactor dynamics and sensor input inform the autonomous control algorithm’s decision-making in a closed-loop manner. The current system is capable of operating at 10 Hz, but faster cycle rates are an area of ongoing research. This test bed will enable NASA and other space vendors to rigorously test their autonomous control systems for NTP rockets under transient (reactor startup and shutdown), steady-state, and fault conditions to reduce development time and risk for autonomous control systems in future missions.

autonomous control

Development for Integrated System-Level Analysis Capabilities in SAM for Molten Salt Reactors

In recent years, there has been renewed interest in Molten Salt Reactors (MSRs) for their potential advantages compared to reactors that rely on solid fuel. In response to such interest, many methods and codes have been developed to capture the unique features of MSRs. Among them, the System Analysis Module (SAM) is a modern system analysis tool that provides fast-running, modest-fidelity, whole-plant transient analysis capabilities, essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. For liquid-fuel MSRs, the complex physics and chemistry involved in MSR operation—such as reactor kinetics, fluid flow, heat transfer, and salt composition dynamics—pose significant challenges for system-level modeling. Specific modeling capabilities are needed for system-level transient simulation. This paper presents recent advancements in SAM capability enhancements for system-level modeling of MSRs, focusing on improved simulation fidelity, computational efficiency, and multi-physics integration. Key enhancements include the development of species transport, Delayed Neutron Precursor (DNP) drift, modified Point Kinetics Equations (PKE), decay heat modeling, key fission product behavior, salt corrosion, and thermal-hydraulic coupling, as well as code robustness and performance enhancements for MSR applications. The code enhancement allows for better predictive accuracy in safety analysis, transient behavior, and operational optimization, thus supporting the design and licensing of next-generation MSRs. Results from case studies are presented to demonstrate the benefits of these enhancements in accurately capturing key reactor transient behaviors.

Hu, Rui (ORCID:0000000237712920)

On the Recoverability of Reactor Dynamics from Point Kinetics Data using SINDYc

Data driven models for reactor dynamics tend to face a few notable challenges. First, the broad range of timescales present across the various feedback mechanisms. Next, high standards for safety and importance of model performance in all operational domains. Finally, the correlations between state variables observed in most transients leads to difficulties when methods attempt to attribute certain dynamic phenomena to a particular cause. The current paper seeks to support efforts towards incorporating physics knowledge into one particular data-driven method for finding reactor dynamics called ``Sparse Identification of Nonlinear Dynamics with Control (SINDYc). The incorporation of physical knowledge into SINDYc will help address the challenges listed above by giving the model an initial understanding of the system being modeled. The demonstration of an exact representation of a set of point reactor dynamics equations in SINDYc is provided. Then, this allows for further discussion with mathematical justification as to why SINDYc, and other data-driven methods, may be difficult to apply to nuclear reactor dynamics due to correlations in the state variables. A particularly useful result of this work is the set of candidate functions required in SINDYc to exactly represent the reactor dynamics under a point approximation. In the future, SINDYc can be integrated with point models for reactor dynamics before being applied to the physical system to yield higher accuracy.

22 - GENERAL STUDIES OF NUCLEAR REACTORS

Comparison of spatial dynamics and point kinetics approaches in multiphysics modeling of the molten salt reactor experiment

In this work, we present validation test results of fully coupled neutronics and thermal-hydraulics models of the Molten Salt Reactor Experiment (MSRE) against experimental data of the zero power pump transients and the natural circulation tests at low power. To capture the strong coupling between neutronics and thermal-hydraulics due to fuel circulation, and to account for the delayed neutron precursor (DNP) distribution, the porous media thermal-hydraulics solver Pronghorn was fully coupled to the spatial neutron dynamics code Griffin, which solves the neutron diffusion equation, and to the 0-D point kinetics solver Squirrel, using a 2-D homogenized representation of the MSRE. The validation test results show very good agreement with experimental data for both point kinetics and spatial dynamics simulations, capturing the strong feedback effect and DNP losses in the MSRE. The 0-D code Squirrel accurately predicted the time-dependent behavior in the MSRE given the steady-state spatial dynamics solution of Griffin.

42 - ENGINEERING

Stochastic Modeling of the Joint Neutron Number-Cumulative Fission Fragment Kinetic Energy Deposition Distribution and its Statistical Moments [Slides]

We investigate the joint distribution of the neutron number and cumulative fission-fragment kinetic energy (FKE) deposition, with a specific focus on low-order statistical moments: the mean, variance, and correlation. Starting from a point-kinetic framework, we derive a forward Master equation (FME) for the joint distribution and develop the corresponding moment equations.

42 ENGINEERING

Three-point Analysis for Butler-Volmer Electrochemical Kinetics

This file contains a spreadsheet and equations that evaluate corrosion test data. The data (which can be inserted by the user) is current vs voltage data. This spreadsheet will be part of the supplemental information of a journal article that is under review. Specifically, the spreadsheet evaluates the classical Butler Volmer equation in the presence of several different forms of noise found in electrochemical systems. The forms of noise are: 1) solution resistance, 2) random noise in the current, 3) drift of the open circuit potential voltage.

Cho, Seongkoo [Lawrence Livermore National Laborat

Structural Aspects of Neutron Survival Probabilities

The neutron survival probability (and related quantities including probabilities of extinction and initiation) is a central element of the broader stochastic theory of neutron populations and finds application in fields including reactor start-up, analysis of reactor power bursts and criticality accidents, and safeguards. In a full neutron transport formulation, the equation governing the single-neutron survival probability is a backward or adjoint-like integro-partial differential equation with the added complexity of being highly nonlinear. Analogous formulations of this equation exist in the context of many approximate theories of neutron transport, with the point kinetics formulation having received significant theoretical attention since the 1940s. This work continues this tradition by providing a novel analysis of the single-neutron survival probability equation using the tools of boundary layer theory. The analysis reveals that the “fully dynamic” solution of the single-neutron survival probability equation—and some key probability distributions derived from it—may be cast as a singular perturbation around the underlying quasi-static single-neutron probability of initiation. In this perturbation solution, the expansion parameter is the ratio of the neutron generation time to a macroscopic time scale characterizing the overall system evolution; this interpretation illuminates some of the fundamental structural aspects of neutron survival phenomena.

97 MATHEMATICS AND COMPUTING

Revisiting a minimally destructive analytic approach for determining electrochemical kinetic parameters: Measuring aluminum corrosion across a wide pH range based on the Butler-Volmer equation

Here, this study revisits the three-point sampling of the simplified Butler-Volmer equation to address the limitations of strong potentiodynamic polarization, which can introduce irreversible damage and uncertainty in corrosion analysis. The method extracts electrochemical kinetic parameters while minimizing polarization effects, evaluates noise sensitivity relative to overpotential, and accounts for errors from signal noise, OCP drift, ohmic resistance, and mass-transfer constraints. Verified against the Tafel extrapolation method for aluminum corrosion across a wide pH range, this low-polarization approach enables accurate evaluations with specific error estimates, offering a robust alternative to linear polarization resistance methods that assume constant Tafel slopes.

36 MATERIALS SCIENCE

Chemistry of Sugar Formation in the Gas Phase: Following the Activated Aldehyde

Sugars are produced by living organisms, and are required building blocks for life as we know it, which raises the foundational question of how sugars formed in a prebiotic environment. The abiotic formose reaction produces sugars from formaldehyde, but our understanding of its initiation step remains murky, with chemists invoking the concept of an “activated aldehyde” to seed this reaction. Singlet hydroxycarbenes, high-energy isomers of aldehydes, were recently reported to facilitate sugar formation under cold, nonaqueous conditions relevant to interstellar environments. Here, we generate singlet methylhydroxycarbene ( 1 CH 3 –C̈–OH) from the photodissociation of pyruvic acid and experimentally measure its gas-phase reaction with d 4 -acetaldehyde using multiplexed photoionization mass spectrometry. The C 4 H 4 D 4 O 2 isomer d 4 -acetoin is the sole product, which we kinetically link to the reactant CH 3 –C̈–OH, and attribute to a carbonyl-ene formation mechanism. We see no evidence of 3-hydroxybutanal, the C–H insertion product expected in carbene chemistry. Using automated exploration we calculate stationary points on the potential energy surface and report master equation rate coefficients from T = 20–600 K, providing quantitative kinetics of this fast reaction for use in chemical models. The prereactive complex in this reaction is stabilized by both hydrogen bonding and electrophilic carbene C═O interactions. These effects create a short-range dynamical bottleneck for the reaction besides the long- and midrange barrierless bottlenecks. Combined with recent reports of 1 HC̈OH production from methanol photodissociation and pyruvic acid production in cold irradiated ices, this work provides evidence that singlet hydroxycarbene + aldehyde chemistry is a feasible path to prebiotic sugar formation.

aldehydes

Nonlinear simulation of under-resolved flows with shocks

Here, we consider the numerical simulation of advection-dominated flows whose wide range of physical length scales exceed the memory capacity of finite computers. Simulating flows with shocks and turbulence presented challenges for the earliest computers that were quickly overcome by the development of new numerical methodology. Principal among those new ideas were artificial viscosity and finite volume methods, concepts that remain in common use today. We begin by describing the history of those methods, the innovators and their motivations. We then describe the development of finite scale theory, a reformulation of Navier–Stokes theory that exposes the physical principles on which artificial viscosity is based. We discuss the essential properties of the finite scale equations, the observer, unresolved kinetic energy and inviscid energy dissipation. We briefly consider the implementation of the finite scale equations on the computer from the point of view of Gisin’s conjectures about finite information.

97 MATHEMATICS AND COMPUTING

Asymptotic-preserving dynamical low-rank method for the stiff nonlinear Boltzmann equation

In kinetic theory, numerically solving the full Boltzmann equation is extremely expensive. This is because the Boltzmann collision operator involves a high-dimensional, nonlinear integral that must be evaluated at each spatial grid point and every time step. The challenge becomes even more pronounced in the fluid (strong collisionality) regime, where the collision operator exhibits strong stiffness, causing explicit time integrators to impose severe stability restrictions. In this paper, we propose addressing this problem through a dynamical low-rank (DLR) approximation. The resulting algorithm requires evaluating the Boltzmann collision operator only r 2 times, where r, the rank of the approximation, is much smaller than the number of spatial grid points. We propose a novel DLR integrator, called the XL integrator, which reduces the number of steps compared to the available alternatives (such as the projector splitting or basis update & Galerkin (BUG) integrator). For a class of problems including the Boltzmann collision operator which enjoys a separation property between physical and velocity space, we further propose a specialized version of the XL integrator, called the sXL integrator. This version requires solving only one differential equation to update the low-rank factors. Furthermore, the proposed low-rank schemes are asymptotic-preserving, meaning they can capture the asymptotic fluid limit in the case of strong collisionality. Our numerical experiments demonstrate the efficiency and accuracy of the proposed methods across a wide range of regimes, from non-stiff (kinetic) to stiff (fluid).

97 MATHEMATICS AND COMPUTING

PyJMAK: An Open-Source Python Toolkit for Modeling Solid-State Metallurgical Phase Transformations

Accurate prediction of metallurgical phase transformations is an essential basis for autonomous optimization and rapid part qualification. Several methods can be used to estimate the evolution of phase fractions such as JMAK kinetics-based models, phase-field models, thermodynamic models, and data-driven machine learning models. Thermodynamic and phase-field-based methodologies solve multiphysics equations requiring numerous calibration parameters and significant computational resources. As a result, the computation domain is limited to a point or on order of micron-meters. The data-driven models rely on large datasets from experiments and simulations. While the JMAK model only provides information about phase fraction evolution, it can predict this evolution in near real-time using thermal history and thermodynamic data without restriction on the domain. JMAK models have been popularly used by researchers to model phase transformations occuring during additive manufacturing or over arbitrary temperature profiles. Commercial proprietary software such as Abaqus and Ansys or closed-source in-house implementations offer the ability to model JMAK based kinetics to predict phase transformation. However, these software packages are not open-source or freely available for use and development in conjunction with manufacturing machines, sensors, and machine learning algorithms. In addition, the use of the model is restricted by a license token. In contrast, given temperature profiles at multiple points in the domain, this Python-based PyJMAK model can compute phase evolution in parallel due to its stand-alone modular, voxel-based structure, and it can be executed on high-performance computing resources without any license restrictions.

Prabhune, Bhagya [Oak Ridge National Laboratory (O

A theoretical kinetic study of ĊH 3 + ṄH 2 : From electronic structure to NH 3 /CH 4 combustion modelling implications

Carbon–nitrogen interaction reactions play an important role in governing the reactivity of ammonia blended fuels. However, there remains uncertainties regarding their detailed reaction pathways and rate constants, hampering the development of high-fidelity chemical kinetic models. In this study, the kinetics of ĊH 3 + ṄH 2 , a key C–N interaction reaction in ammonia/methane blend combustion have been investigated. The potential energy surface has been explored using the high-level ANL0F method, yielding highly accurate stationary point energies that agree with ATcT values within 0.1 kcal mol –1 . Variable reaction coordinate transition state theory is used to treat the barrierless association and decomposition reaction channels, based on directly sampled radical-radical interaction energies at the CASPT2-F12(2e,2o)/cc-pVTZ-F12 level of theory. The minimum transitional mode numbers of states obtained are then coupled with the RRKM/master equation to calculate temperature- and pressure-dependent rate constants. Our a priori calculations capture available experimental measurements from the literature very well. The calculated rate constants have been incorporated into an NH 3 /CH 4 chemical kinetic model currently under development at the University of Galway. The effect of the updated kinetic data for ĊH 3 + ṄH 2 on model predicted NH 3 /CH 4 fuel reactivity is elucidated.

ab initio

Mean-field dynamo as a quantum-like modulational instability

Presented here is a novel formulation of the mean-field dynamo as a modulational instability of magnetohydrodynamic (MHD) turbulence. This formulation, termed mean-field wave kinetics (MFWK), is based on the Weyl symbol calculus and allows describing the interaction between the mean fields (magnetic field and fluid velocity) and turbulence without requiring scale separation that is commonly assumed in the literature. The turbulence is described by the Wigner–Moyal equation for the spectrum of the two-point correlation matrix (Wigner matrix) of magnetic-field and velocity fluctuations and depicts the turbulence as an effective plasma of quantum-like particles that interact via the mean fields. Eddy–eddy interactions, which serve as ‘collisions’ in this effective plasma, are modelled within the standard minimal tau approximation to aid comparison with existing theories. Using MFWK, the non-local electromotive force is calculated for generic turbulence from first principles, modulo the limitations of MFWK. This result is then used to study, both analytically and numerically, the modulational modes of MHD turbulence, which appear as linear instabilities of the said effective quantum-like plasma of fluctuations. The standard α 2 -dynamo and other known results are reproduced as special cases. A new dynamo effect is predicted that is driven by correlations between the turbulent flow velocity and the turbulent current.

astrophysical plasmas

Trends in spatial correlations, two-phase coexistence, and criticality in a class of type-2 Schloegl models for autocatalysis

A class of type-2 Schloegl models is considered for particles on a square lattice with variable-range cooperativity. These models involve: (i) spontaneous particle annihilation at rate p; (ii) autocatalytic particle creation at unoccupied sites (i, j) with n ⩾ 2 particles within a specified neighborhood, Ω 𝑁 (i, j), of sites at rate $k_n$ = $\frac{^{(^n_2)}}{_{(^N_2)}}$ = $\frac{n{(n-1)}}{_{N(N-1)}}$; and (iii) possible spontaneous particle creation at unoccupied sites at “small” rate ɛ ⩾ 0. In some cases, Ω 𝑁 just includes all symmetry-equivalent sites at a single specific distance 𝑑 (in units of lattice constants) from the unoccupied site, e.g., 𝑑 = 1 (nearest-neighbor sites) where 𝑁 = 4, or 𝑑 = √5 (or √13 or…) where 𝑁 = 8. In other cases, Ω 𝑁 includes sites multiple distances from the unoccupied site, e.g., 𝑑 = {1,√2}, where 𝑁 = 8. Kinetic Monte Carlo (KMC) simulation reveals that these models exhibit a nonequilibrium discontinuous phase transition between high- and low-density states below a critical point, ɛ < ɛ c , with generic two-phase coexistence (2PC) at least for smaller 𝑁. With some exceptions, there is an approach toward mean-field behavior with increasing 𝑁 (so the regime of generic 2PC shrinks, and ɛ c approaches the mean-field value of 1/27). Additional insight into trends is provided by analysis of the exact master equations for the models via hierarchical truncation. These truncations utilize suitably tailored pair approximations which reflect the dominant nonequilibrium spatial correlations. These correlations in turn are shown to reflect the details of the autocatalytic particle creation process. For spatially heterogeneous states, the truncations produce coupled sets of lattice differential equations (LDE) which can describe orientation-dependent propagation of an interface between high- and low-density steady states for ɛ < ɛ c . Pair approximation values of 𝑝 = 𝑝 eq where the interface is stationary, and its orientation-dependence, are in semiquantitative agreement with KMC results. In conclusion, this comparison accounts for propagation failure in the LDE which complicates interpretation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Reactive Modified Epoxy Resin and Its Miscible Blends Based on Recycled Oligomers from Solvolysis

Chemical depolymerization of fully cured epoxy resin with 20% reactive modifier was successfully performed via a solvent-assisted solvolysis process into low molecular weight recyclable oligomers (RO) at 240 °C in a pressure vessel at 650 psi for 4 h. The thermoset epoxy resin was depolymerized into transparent brown viscous fluid with a higher viscosity than the uncured epoxy resin with approximately 93% yield. Different concentrations of the RO were homogeneously mixed with the pure epoxy resin, and their curing kinetics, viscosity, FTIR, mechanical properties, DMA, and cross-link density were investigated. The curing kinetics of the pure reactive modified epoxy resin (baseline) and its mixtures with RO of different concentrations were investigated under both isothermal and nonisothermal conditions using small amplitude oscillatory shear flow. The elastic and viscous moduli (G′ and G″), complex viscosity (η*), and tan δ values were evaluated at different curing times and temperatures. The G′, G″, and η* increased dramatically, while tan δ decreased strongly by several orders of magnitude at the gel point. The zero-shear viscosity (η 0 ) was determined from the angular frequency dependent on η* based on the Cross model for different blend compositions in the liquid state before curing. The composition dependence of η 0 showed a positive deviation from the linear mixing rule and was well described by the Lecyar model. Here, the apparent activation energy of curing (E a ) was also evaluated according to the Arrhenius equation and was found to be 46 ± 2 kJ/mol regardless of the different contents of RO. For all blends up to 40 wt % RO, only one tan δ peak systematically shifting to lower temperatures with increasing content of RO was observed in the DMA measurements, indicating that the epoxy resin and the RO are miscible with up to 40 wt % RO.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Kinetic Monte Carlo simulations of aging in δ -Pu

We have developed a first-passage kinetic Monte Carlo approach for materials aging to investigate the sensitivity of void swelling to model parameters, including helium bubble density and size distribution. In addition to explicitly accounting for the spatial distribution of individual point defects, bubbles, and voids, our approach can simulate total doses equivalent to 100 years of natural aging on statistically representative volumes of materials. This technique enables us to study the effects on swelling and radiation damage evolution due to temperature and dose rate (as altered in artificially aged experiments), differences in effective interaction radii between vacancies and interstitials, and varying defect diffusion activation energies, while providing more detailed information than previous rate-equation based approaches. In conclusion, our results indicate that spatial effects that are not modeled in mean-field rate theories could play a significant role in void swelling initiation and growth for certain regimes of model parameters.

Actinides