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DOE OSTI2021

Glass Property-Composition Models for Support of Hanford WTP LAW Facility Operation

Current plans for the River Protection Project envision starting to vitrifying low-activity waste (LAW) by 2023 using a Direct Feed Low-Activity Waste (DFLAW) approach and subsequently using a full-pretreatment approach. The Hanford Tank Waste Treatment and Immobilization Plant (WTP) LAW Facility will be operated and controlled using a LAW glass formulation algorithm (GFA), which requires several inputs based on research and development results. LAW glass property-composition models for several product quality and processing properties are key inputs for the LAW GFA. It is envisioned that the preliminary LAW GFA discussed by Kim and Vienna (2012) will be used for commissioning and initial radioactive operations of the WTP LAW Facility under Bechtel National, Inc. using the DFLAW approach. Then, an updated LAW GFA will be developed for implementation by the WTP operating contractor that takes over after WTP LAW Facility commissioning. This report documents the enhanced LAW glass property-composition models developed for use in the updated LAW GFA. The properties for which models were developed include Product Consistency Test (PCT) response, Vapor Hydration Test (VHT) response, viscosity at 1150 °C, electrical conductivity at 1150 °C, melter SO3 tolerance at 1150 °C, and K-3 refractory corrosion at 1208 °C. Table S.1 lists the tables in this report that contain the recommended models for each of these properties. The model types recommended include partial quadratic mixture (PQM) models for viscosity, electrical conductivity, melter SO 3 tolerance and K-3 corrosion, bias corrected PQM model (bcPQM) for PCT, and logistic PQM model for VHT. The fits of model and validation subsets were found to be well predicted by the recommended models.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

Effect of constitutive law on the erythrocyte membrane response to large strains

Three constitutive laws, that is the Skalak, neo-Hookean and Yeoh laws, commonly employed for describing the erythrocyte membrane mechanics are theoretically analyzed and numerically investigated to assess their accuracy for capturing erythrocyte deformation characteristics and morphology. In this work, particular emphasis is given to the nonlinear deformation regime, where it is known that the discrepancies between constitutive laws are most prominent. Hence, the experiments of optical tweezers and micropipette aspiration are considered here, for which relationships between the individual shear elastic moduli of the constitutive laws can also be established through analysis of the tension-deformation relationship. All constitutive laws were found to adequately predict the axial and transverse deformations of a red blood cell subjected to stretching with optical tweezers for a constant shear elastic modulus value. As opposed to Skalak law, the neo-Hookean and Yeoh laws replicated the erythrocyte membrane folding, that has been experimentally observed, with the trade-off of sustaining significant area variations. For the micropipette aspiration, the suction pressure-aspiration length relationship could be excellently predicted for a fixed shear elastic modulus value only when Yeoh law was considered. Importantly, the neo-Hookean and Yeoh laws reproduced the membrane wrinkling at suction pressures close to those experimentally measured. None of the constitutive laws suffered from membrane area compressibility in the micropipette aspiration case.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Discovering exact, gauge-invariant, local energy-momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds

Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas. However, exact local energy-momentum conservation laws for the electromagnetic gyrokinetic system have not been found despite the continuous effort. Without such local conservation laws, energy and momentum can be instantaneously transported across spacetime, which is unphysical and casts doubt on the validity of numerical simulations based on the gyrokinetic theory. The standard Noether procedure for deriving conservation laws from corresponding symmetries does not apply to gyrokinetic systems because the gyrocenters and electromagnetic fields reside on different manifolds. To overcome this difficulty, we develop a high-order field theory on heterogeneous manifolds for classical particle-field systems and apply it to derive exact, local conservation laws, in particular the energy-momentum conservation laws, for the electromagnetic gyrokinetic system. A weak Euler-Lagrange equation is established to replace the standard Euler-Lagrange equation for the particles. It is discovered that an induced weak Euler-Lagrange current enters the local conservation laws. And it is the new physics captured by the high-order field theory on heterogeneous manifolds. A recently developed gauge-symmetrization method for high-order electromagnetic field theories using the electromagnetic displacement-potential tensor is applied to render the derived energy-momentum conservation laws electromagnetic gauge-invariant.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Uncertainty Quantification of a Light Water Pulsed-Neutron Die-Away Experiment to Thermal Neutron Scattering Laws

Thermal neutron scattering laws are important nuclear data for many nuclear science and engineering applications. Validation helps to ensure that a thermal neutron scattering law has a high quality and often employs critical benchmarks as integral experiments. Recently, pulsed-neutron die-away benchmarks have been used as an experiment to validate thermal neutron scattering laws. Herein, we evidence how this alternative integral experiment has a high sensitivity to these nuclear data by performing an uncertainty quantification analysis. The analysis randomly sampled the nuclear model parameters associated with hydrogen bound in light water thermal neutron scattering law and sampled other nuclear data that influenced the experiment’s integral parameter (e.g., elastic scattering, absorption in hydrogen and oxygen) from their respective covariance matrices. The thermal neutron scattering law caused an uncertainty in the integral parameter that reached 2.67%, which exceeds by an order of magnitude the uncertainties induced in commonly used thermal solution critical benchmarks. The validation performed here, although limited due to a poor description of the historical experiment, indicated that the ENDF/B-VIII.0 thermal neutron scattering law well predicted the integral parameter. These results motivate further benchmark and validation efforts using pulsed-neutron die-away experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Kink solutions with power law tails

We present a comprehensive review about the various facets of kink solutions with a power law tail, which have received considerable attention during the last few years. This area of research is in its early stages; although several aspects have become clear by now, there are a number of issues which have only been partially understood or not understood at all. We first discuss the aspects which are reasonably well known and then address in some detail the issues which are only partially or not understood at all. We present a wide class of higher (than sixth) order field theory models admitting implicit kink as well as mirror kink solutions where the two tails facing each other have a power law or a power-tower type fall off, whereas the other two ends not facing each other could have either an exponential or a power law tail. The models admitting implicit kink solutions where the two ends facing each other have an exponential tail while the other two ends have a power law tail are also discussed. Moreover, we present several field theory models which admit explicit kink solutions with a power law fall off; we note that in all these polynomial models while the potential V ( ϕ ) is continuous, its derivative is discontinuous. We also discuss one of the most important and only partially understood issues of the kink–kink and the kink–antikink forces in case the tails facing each other have a power law fall off. Finally, we briefly discuss the kink–antikink collisions at finite velocity and present some open questions.

power-tower tail↗

DOE OSTI2020

Theoretical power-law relationship between permeability and formation factor

Permeability k and formation factor F are important petrophysical properties that have broad applications to reservoir engineering. Although well-log analysis has advanced reservoir characterizations, direct measurement of k is still not available. Accordingly, resistivity logs and more particularly formation factor have been frequently used to estimate k. In this study, we present a theoretical framework to relate k to F. We use power-law scaling from continuum percolation theory to develop a theoretic relationship between k and F, which is similar in form to a published power-law equation with empirical coefficients. Our result gives a physical interpretation to this empirical relationship. We also compare power-law scaling laws from percolation theory with data derived from experimental measurements and numerical simulations in the literature. Finally, using the Curve Fitting toolbox of MATLAB, the parameters of the power-law equations are determined, and the significance of the non-universal power laws are discussed.

42 ENGINEERING↗

DOE OSTI2023

Seeing through noise in power laws

Despite widespread claims of power laws across the natural and social sciences, evidence in data is often equivocal. Modern data and statistical methods reject even classic power laws such as Pareto’s law of wealth and the Gutenberg–Richter law for earthquake magnitudes. We show that the maximum-likelihood estimators and Kolmogorov–Smirnov (K-S) statistics in widespread use are unexpectedly sensitive to ubiquitous errors in data such as measurement noise, quantization noise, heaping and censorship of small values. This sensitivity causes spurious rejection of power laws and biases parameter estimates even in arbitrarily large samples, which explains inconsistencies between theory and data. We show that logarithmic binning by powers of λ > 1 attenuates these errors in a manner analogous to noise averaging in normal statistics and that λ thereby tunes a trade-off between accuracy and precision in estimation. Binning also removes potentially misleading within-scale information while preserving information about the shape of a distribution over powers of λ, and we show that some amount of binning can improve sensitivity and specificity of K-S tests without any cost, while more extreme binning tunes a trade-off between sensitivity and specificity. We therefore advocate logarithmic binning as a simple essential step in power-law inference.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

Seeing through noise in power laws

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Melter Tests to Define LAW Halide Concentrations, Phase 2

The present work represents the second of two phases to address the formation of secondary sulfate phases while processing high waste loading LAW formulations with elevated halide, chromium, and phosphate feed concentrations over a wide range of LAW waste types, including those with high potassium concentrations. The Test Plan for the present work outlines a series of tests designed to assess the formation of secondary phases over a range of sulfur and halide concentrations for two LAW streams and associated glass formulations as well as crucible testing to identify additives that have the potential to suppress the formation of secondary phases for wastes with high chlorine contents. The combined results from both phases of testing and from previous tests with these LAW waste streams will be used as inputs to future work to develop concentration limits for these components in the LAW glass property composition models and to support the modification and updating of the current WTP LAW glass formulation algorithm.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

A simple generalization of the energy gap law for nonradiative processes

For more than 50 years, an elegant energy gap (EG) law developed by Englman and Jortner [Mol. Phys. 18, 145 (1970)] has served as a key theory to understand and model the nearly exponential dependence of nonradiative transition rates on the difference of energy between the initial and final states. This work revisits the theory, clarifies the key assumptions involved in the rate expression, and provides a generalization for the cases where the effects of temperature dependence and low-frequency modes cannot be ignored. For a specific example where the low-frequency vibrational and/or solvation responses can be modeled as an Ohmic spectral density, a simple generalization of the EG law is provided. Test calculations demonstrate that this generalized EG law brings significant improvement over the original EG law. Both the original and generalized EG laws are also compared with the stationary phase approximations developed for electron transfer theory, which suggests the possibility of a simple interpolation formula valid for any value of EG.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study

Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for understanding these scaling laws remains underdeveloped. In this paper, we explore the neural scaling laws for deep operator networks, which involve learning mappings between function spaces, with a focus on the Chen and Chen style architecture. These approaches, which include the popular Deep Operator Network (DeepONet), approximate the output functions using a linear combination of learnable basis functions and coefficients that depend on the input functions. We establish a theoretical framework to quantify the neural scaling laws by analyzing its approximation and generalization errors. We articulate the relationship between the approximation and generalization errors of deep operator networks and key factors such as network model size and training data size. Moreover, we address cases where input functions exhibit low-dimensional structures, allowing us to derive tighter error bounds. These results also hold for deep ReLU networks and other similar structures. Our results offer a partial explanation of the neural scaling laws in operator learning and provide a theoretical foundation for their applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Self-similar Reynolds-averaged mechanical–scalar turbulence models for Rayleigh–Taylor mixing induced by power-law accelerations in the small Atwood number limit

Analytical self-similar solutions to two-, three-, and four-equation Reynolds-averaged mechanical–scalar turbulence models describing turbulent Rayleigh–Taylor mixing driven by a temporal power-law acceleration are derived in the small Atwood number (Boussinesq) limit. The solutions generalize those previously derived for constant acceleration Rayleigh–Taylor mixing for models based on the turbulent kinetic energy K and its dissipation rate ε, together with the scalar variance S and its dissipation rate χ [O. Schilling, “Self-similar Reynolds-averaged mechanical–scalar turbulence models for Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing in the small Atwood number limit,” Phys. Fluids 33, 085129 (2021)]. The turbulent fields are expressed in terms of the model coefficients and power-law exponent, with their temporal power-law scalings obtained by requiring that the self-similar equations are explicitly time-independent. Mixing layer growth parameters and other physical observables are obtained explicitly as functions of the model coefficients and parameterized by the exponent of the power-law acceleration. Values for physical observables in the constant acceleration case are used to calibrate the two-, three-, and four-equation models, such that the self-similar solutions are consistent with experimental and numerical simulation data corresponding to a canonical (i.e., constant acceleration) Rayleigh–Taylor turbulent flow. The calibrated four-equation model is then used to numerically reconstruct the mean and turbulent fields, and turbulent equation budgets across the mixing layer for several values of the power-law exponent. Finally, the reference solutions derived here can be used to understand the model predictions for strongly accelerated or decelerated Rayleigh–Taylor mixing in the large Reynolds number limit.

42 ENGINEERING↗

DOE OSTI2020

The Floating Chameleon: Floating Nuclear Power Plants and the Nexus of Maritime and Nuclear Security Law

During the 63rd regular session of the International Atomic Energy Agency (IAEA) General Conference, as part of Norway's statement to the General Conference, Mr. Auden Halvorsen, State Secretary for Norway, made the following statement about transportable nuclear power plants (TNPPs): "Deployment of transportable nuclear power plants—TNPPs—demands our attention. The Agency must intensify its conversations of all aspects of the safety and security of such facilities. . . . The scope and applicability of existing requirements and instruments need to be clarified and developed including dialogue with the International Maritime Organization [IMO]." Ensuring the security of TNPPs is essential for their deployment and implementation. TNPPs may be floating nuclear power plants (FNPPs), which bring together elements of nuclear security related to the nuclear power plant with elements of maritime security. Insofar as an FNPP weds the principles of nuclear and maritime security, it also weds the two domains, the ancient traditions and contemporary practices of maritime law with the contemporary practices of nuclear law. Fundamentally, this raises the question, what are the legal requirements for the security of a FNPP? Although both maritime law and nuclear law have established regimes for security through various legal instruments, does an FNPP expose gaps between the current international legal instruments? The previous question of whether international legal regimes define requirements for the security of FNPPs, but a threshold question remains: what is an FNPP? For purposes of nuclear and maritime security, is an FNPP a facility, is an FNPP a vessel and therefore a transport, or does an FNPP change its status based upon temporal and spatial considerations such as when it is docked at a port generating power or in transit to its destination? This set of questions, and others addressed later in this article, highlights that the issue is not merely a question about security but intersects elements of safety whether an FNPP is in uncharted waters of the international regime for both nuclear and maritime law. Here, this paper addresses many of the questions posed above related to the security regulations for an FNPP.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2021

Comprehensive framework for data-driven model form discovery of the closure laws in thermal-hydraulics codes

The two-phase two-fluid model is a basis of many thermal-hydraulics codes used in design, licensing, and safety considerations of nuclear power plants. Thermal-hydraulics codes rely on the closure laws to close the system of conservation equations and describe the interactions between phases. These laws, derived from years of experimental investigations, are semi-empirical correlations that lack generality and have a limited range of applicability. Increase of computational power, availability of new experiments, and development of high-fidelity simulations has increased the number of validation data. The discrepancies between the code predictions and the validation data are a great source of knowledge. Missing physics that are not included in the model but are important for the considered phenomena can be discovered by propagating the information from the experimental results through the model. Furthermore, physics-discovered data-driven model form (P3DM) methodology integrates available integral effect tests and separate effects tests to determine the necessary corrections to the model form of the closure laws. In contrast to existing calibration techniques, the methodology modifies the functional form of the closure laws. Based on the functional form of the correction, the missing physics that were not included in the original model can be discovered. The methodology provides the alternative to the machine learning approach, in which the model is discovered in the form of the intractable black-box relation. In this work, the methodology was applied to the CTF subchannel code to improve the prediction of the two-phase flow phenomena.

42 ENGINEERING↗

DOE OSTI2022

Performance Analysis of Speculative Parallel Adaptive Local Timestepping for Conservation Laws

Stable simulation of conservation laws, such as those used to model fluid dynamics and plasma physics applications, requires the satisfaction of the so-called Courant-Friedrichs-Lewy condition. By allowing regions of the mesh to advance with different timesteps that locally satisfy this stability constraint, significant work reduction can be attained when compared to a time integration scheme using a single timestep size. However, parallelizing this algorithm presents considerable difficulty. Since the stability condition depends on the state of the system, dependencies become dynamic and potentially non-local. In this article, we present an adaptive local timestepping algorithm using an optimistic (Timewarp-based) parallel discrete event simulation. We introduce waiting heuristics to limit misspeculation and a semi-static load balancing scheme to eliminate load imbalance as parts of the mesh require finer or coarser timesteps. Last, we outline an interface for separating the physics of the specific conservation law from the temporal integration allowing for productive adoption of our proposed algorithm. We present a misspeculation study for three conservation laws, demonstrating both the productivity of the local timestepping API, for which 74% of the lines of code are reused across different conservation laws, and the robustness of the waiting heuristics—at most 1.5% of element updates are rolled back. Our performance studies demonstrate up to a 2.8× speedup versus a baseline unoptimized local timestepping approach, a 4x improvement in per-node throughput compared to an MPI parallelization of synchronous timestepping, and scalability up to 3,072 cores on NERSC’s Cori Haswell partition.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Henry’s law constants (IUPAC Recommendations 2021)

Henry’s law states that the abundance of a volatile solute dissolved in a liquid is proportional to its abundance in the gas phase. It applies at equilibrium and in the limit of infinite dilution of the solute. For historical reasons, numerous different definitions, names, and symbols are used in the literature to express the proportionality coefficient, denoted the “Henry’s law constant”. Furthermore, a consistent set of recommendations is presented. An important distinction is made between two new recommended reciprocal quantities: “Henry’s law solubility constant” (H s ) and “Henry’s law volatility constant” (H v ). Eight recommended variants of H s and H v are described and relations among them presented.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Evaluating Impacts of the Inflation Reduction Act and Bipartisan Infrastructure Law on the U.S. Power System

The Inflation Reduction Act of 2022 (IRA) and the Infrastructure Investment and Jobs Act of 2021, commonly referred to as the 'Bipartisan Infrastructure Law (BIL),' collectively represent the largest commitment of the U.S. Federal Government to invest in the modernization and decarbonization of the U.S. energy system. The Congressional Budget Office (CBO) estimates that total support for the broad range of climate and clean energy programs, tax credits, and other incentives authorized through the two laws will exceed $430 billion from 2022 through 2031 (CRS 2022; CBO 2021, 2022). While the climate and clean energy provisions are numerous and have the potential to impact all aspects of the U.S. energy system from fuel and electricity production to final consumption in industry, transportation, and buildings, the provisions relevant to the electricity sector - in particular the suite of tax credits for clean generation, storage, and carbon dioxide ( CO 2 ) capture and storage - are expected to be some of the most consequential in terms of emissions reduction and clean energy deployment (Larsen et al. 2022; Jenkins, Mayfield, et al. 2022; Mahajan et al. 2022; Zhao et al. 2022). In this report, we detail the methods and results of a study estimating the potential impacts of key provisions of IRA and BIL on the contiguous U.S. power sector from present day through 2030. The analysis employs an advanced power system planning model, the Regional Energy Deployment System (ReEDS), to evaluate how major provisions from both laws impact investment in and operation of utility-scale generation, storage, and transmission, and, in turn, how those changes impact power system costs, emissions, and climate and health damages. While not exhaustive in capturing every provision, the analysis estimates the possible scale of power-sector impacts that could result from the modeled provisions in IRA and BIL. The study is structured around two scenarios to evaluate the potential impacts of both laws on the power sector: 1) No New Policy: A counter-factual scenario that reflects all Federal and state policies enacted as of September 2022, with exception to IRA and BIL, and assumes load growth consistent with the Energy Information Administration's Annual Energy Outlook 2022 (AEO22) Reference case (EIA 2022a); 2) IRA-BIL: A scenario reflecting all Federal and state policies enacted as of September 2022, including key IRA and BIL provisions, most notably the investment and production tax credits for zero-carbon emitting electricity generation and storage (ITC and PTC), the tax credit for CO 2 capture and storage (45Q), and the tax credit for existing nuclear plants (described further in Section 2.3). To account for the impacts of IRA and BIL on electrification, assumes increased load growth consistent with a scaled version of the Medium Electrification scenario from the Electrification Futures Study (Mai et al. 2018). These scenarios are simulated across seven sets of assumptions with varying projected future electricity market conditions, including technology costs and performance, natural gas prices, and the degree of availability, feasibility, and cost of development of renewable resources, electricity transmission, and CO 2 pipeline, injection, and storage infrastructure. In addition, we simulate two sensitivities on the 'policy' treatment in which we vary key assumptions pertaining to the realized value of the clean electricity ITC and PTC: 1) the cost of monetization of tax credits, and 2) the level of bonus crediting realized by project developers. We demonstrate that IRA and BIL have the collective potential to drive substantial growth in clean electricity by 2030, while reducing costs for consumers, mitigating climate change, and decreasing the human health impacts of power sector emissions. However, we also demonstrate that if expected cost improvements of clean technologies are not realized and/or constraints on deployment driven by factors such as supply-chain challenges, regulatory hurdles, and the social acceptability of energy infrastructure development limit the rate of clean energy and associated infrastructure deployment (such as transmission), then the share of clean generation achieved and the associated emissions benefits realized may be substantively reduced.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

Emergent area laws from entangled matrices

We consider a wavefunction of large N matrices supported close to an emergent classical fuzzy sphere geometry. The SU( N ) Gauss law of the theory enforces correlations between the matrix degrees of freedom associated to a geometric subregion and their complement. We call this ‘Gauss law entanglement’. We show that the subregion degrees of freedom transform under a single dominant, low rank representation of SU( N ). The corresponding Gauss law entanglement entropy is given by the logarithm of the dimension of this dominant representation. It is found that, after coarse-graining in momentum space, the SU( N ) Gauss law entanglement entropy is proportional to the geometric area bounding the subregion. The constant of proportionality goes like the inverse of an emergent Maxwell coupling constant, reminiscent of gravitational entropy.

1/N Expansion↗