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DOE OSTI2020

Pressure-stabilized divalent ozonide CaO 3 and its impact on Earth's oxygen cycles

High pressure can drastically alter chemical bonding and produce exotic compounds that defy conventional wisdom. Especially significant are compounds pertaining to oxygen cycles inside Earth, which hold key to understanding major geological events that impact the environment essential to life on Earth. Here we report the discovery of pressure-stabilized divalent ozonide CaO3 crystal that exhibits intriguing bonding and oxidation states with profound geological implications. Our computational study identifies a crystalline phase of CaO 3 by reaction of CaO and O 2 at high pressure and high temperature conditions; ensuing experiments synthesize this rare compound under compression in a diamond anvil cell with laser heating. High-pressure x-ray diffraction data show that CaO 3 crystal forms at 35 GPa and persists down to 20 GPa on decompression. Analysis of charge states reveals a formal oxidation state of -2 for ozone anions in CaO 3 . These findings unravel the ozonide chemistry at high pressure and offer insights for elucidating prominent seismic anomalies and oxygen cycles in Earth’s interior. We further predict multiple reactions producing CaO 3 by geologically abundant mineral precursors at various depths in Earth’s mantle.

58 GEOSCIENCES↗

DOE OSTI2022

Exact quantum scars in the chiral nonlinear Luttinger liquid

While the chiral linear Luttinger liquid is integrable via bosonization, its nonlinear counterpart does not admit for an analytic solution. In this work, we find a subextensive number of exact eigenstates for a large family of density-density interaction terms. These states are embedded in a continuum of strongly correlated excited states. The real-space entanglement entropy of some exact states scales logarithmically with system size while that of others has volume-law scaling. We introduce momentum-space entanglement as an unambiguous differentiator between these exact states and the remaining excited states. With regard to momentum space, the exact states behave as bona fide quantum many-body scars: they exhibit identically zero momentum-space entanglement, while typical eigenstates behave thermally. We corroborate this finding by a level statistics analysis. Here we detail the general formalism for systematically finding all interaction terms and associated exact states, and present a number of infinite exact state sequences extending to arbitrarily high energies. Unlike many previous examples of quantum many-body scars, the exact states uncovered here do not lie at equidistant energies and do not follow from a special operator algebra. Instead, they are uniquely enabled by the interplay of Fermi statistics and chirality.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Direct quarkonium production in DIS from a joint CGC and NRQCD framework

We compute the differential cross section for direct quarkonium production in high-energy electron-nucleus collisions at small 𝑥. Our computation is performed within the nonrelativistic QCD factorization formalism that separates the calculation into short distance coefficients and long distance matrix elements that depend on the color and spin of the state. We obtain the short distance coefficients of the production of the heavy quark pair within the framework of the color glass condensate effective field theory, which resums coherent multiple interactions of the heavy quark pair with the nucleus to all orders. Our results are expressed as the convolution of perturbatively calculable functions with multipoint lightlike Wilson line correlators. In the correlation limit, we establish the correspondence between our color glass condensate formulation with calculations employing the transverse momentum dependent (TMD) framework. We extend this correspondence by resumming kinematic power corrections within the improved TMD framework, which interpolates between the TMD formalism and 𝑘 ⊥ -factorization formalism. We present a detailed numerical analysis, focusing on 𝐽/𝜓 production in the kinematics accessible at the future Electron-Ion Collider, highlighting the importance of genuine higher-order saturation contributions when the electron collides with a large nucleus. Our results are also valid in the photoproduction limit where we expect the largest contribution from genuine higher-order saturation contributions which could be accessed in ultraperipheral collisions of relativistic heavy ions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Applying Quantum Tomography to Hadronic Interactions

A proper description of inclusive reactions is expressed with density matrices. Quantum tomography reconstructs density matrices from experimental observables. We review recent work that applies quantum tomography to practical experimental data analysis. Almost all field-theoretic formalism and modeling used in a traditional approach is circumvented with great efficiency. Tomographically-determined density matrices can express information about quantum systems which cannot in principle be expressed with distributions defined by classical probability. Topics such as entanglement and von Neumann entropy can be accessed using the same natural language where they are defined. A deep relation exists between separability, as defined in quantum information science, and factorization, as defined in high energy physics. Factorization acquires a non-perturbative definition when expressed in terms of a conditional form of separability. An example illustrates how to go from data for momentum 4-vectors to a density matrix while bypassing almost all the formalism of the Standard Model.

Martens, J. C.↗

DOE OSTI2024

Drop Analysis of a Department of Energy Standard Canister Containing Fort Saint Vrain SNF– 24138

DOE manages over 300 types of SNF, many of which are located at the INL site. Managing this large variety of SNF for storage, transportation, and disposal poses a challenge to DOE. The Idaho Cleanup Project and INL are collaborating on the DOE SNF Road-Ready Demonstration (“Road-Ready Demonstration”), which will develop and demonstrate the designs, technology, processes, and regulatory framework for packaging DOE-managed SNF for “road-ready dry storage.” Road-ready dry storage (RRDS) is an SNF management concept in which SNF is packaged into dry, sealed canisters that are then placed in on-site storage in anticipation of later transport and disposition. The forward-looking goal of the Road-Ready Demonstration is to establish the foundation for a large-scale RRDS program at the INL site. One critical aspect of RRDS is the ability to certify the DOE Standard Canister and its associated transportation package in accordance with 10 CFR 71 for offsite transportation. Depending on the SNF type and transportation strategy, DOE Standard Canisters may be required to maintain structural integrity under hypothetical accident scenarios (e.g., drop events). The DOE Standard Canisters have been tested and analyzed under various SNF loading configurations and accident drop events in support of the Idaho Spent Fuel Facility and other DOE programs; however, no analysis has yet been completed in support of the recently initiated Road-Ready Demonstration. This paper presents preliminary results from a finite element analysis of the Ø45.7 cm × 4.6 m (Ø18 in. × 15 ft) DOE Standard Canister under the 9 m drop at 80 degrees off-vertical drop scenario considered in previous INL tests and analyses. It considers the Fort St. Vrain spent nuclear fuel loading configuration proposed for the Road-Ready Demonstration, uses updated material properties, and applies the strain-based acceptance criteria established in ASME Boiler and Pressure Vessel Code’s Section III, Division 3 rules for storage and transportation spent nuclear fuel containments. This updated analysis is compared to previous DOE Standard Canister drop analyses. Preliminary results from the updated analysis show that certain regions of the containment exceed the allowable limits during the accidental drop event. However, these regions are limited to components performing a non-structural function. While further work on this analysis will be pursued, this analysis serves as the foundation for formal calculations used to support applicable certification efforts of the RRDS system at INL.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2024

01-16 DOE Authorization Strategy

DOE-STD-1189-2016 Process Standard – Stage Gates Establishment of Regulatory Requirements Clarity of Path Forward Integration of Safety and Design Reduce Project Risk by Establishing Regulatory Certainty through formal regulatory approvals. Flexibility in risk analysis and presentation methods. ANSI/ANS 15.21, DOE-STD-3009, LMP/TICAP

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

MFANS 2024 - Formally Proving Characteristics of Cyber-Physical Systems

Cyber-physical systems (CPS) are engineered systems that rely on the smooth integration of computational algorithms and physical elements. This integration presents new challenges for verifying that systems will behave as expected. The goal of this presentation is to present current challenges and potential solutions for the formal verification of cyber-physical systems. For cyber systems, formal methods refer to systematically rigorous mathematical techniques employed in the specification, development, analysis, and verification of both software and hardware systems. Recent advancements in computer science have yielded sophisticated tools specifically designed to address challenges associated with formal methods in complex systems. These tools leverage various foundational concepts such as logic, formal languages, program semantics, type systems, type theory, and automata theory. A notable achievement in the application of formal methods is the seL4 microkernel, claimed to be the first general-purpose operating-system kernel to be verified. Its proof implies the absence of bugs and guarantees that the kernel meets specifications. For physical systems, dynamic and control theory has a history of using rigorous analytic techniques to prove functional correctness. Lyapunov, optimal, classical, modern, and robust control theories all provide rigorous mathematical methods both to analyze system performance and to design controller that can be guaranteed to meet certain objectives. Recent computational techniques like level set theory and reachability analysis provide assertions that a system's state will avoid unsafe regions. Even though success has been independently achieved for cyber systems and physical systems, the integration of such systems creates new challenges. In particular, there is an obvious discrepancy between finite-state machines and infinite-state systems, resulting in different approaches for modeling and analyzing these system. While it is possible to simulate hybrid systems, this provides only a demonstration of a performance and not proof. For hybrid systems, current formal methods and system analysis approaches typically require a workarounds to work on hybrid systems like CPS. This paper will outline the state of the art and limits of current practice for formally verifying CPS and will identify possible research directions that require attention.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Evaluation of Joint Cyber/Safety Risk in Nuclear Power Systems

This report presents an analysis of the Emergency Core Cooling System (ECCS) for a generic Boiling Water Reactor (BWR)-4 NPP. The Electric Power Research Institute (EPRI) developed Hazards and Consequences Analysis for Digital Systems (HAZCADS) process is applied to the ECCS and its subsystems to identify unsafe control actions (UCAs) which act as possible cyber events of concern. The analysis is performed for two design basis events: Small-break Loss of Coolant Accident (SLOCA) and general transients (TRANS), such as unintended reactor trip. In previous work, HAZCADS UCAs were combined with other cyber-attack analysis to develop a risk-informed approach; however, this was for a single system. This report explores advanced systems engineering modeling approaches to model the interactions between digital assets across multiple systems which may be targeted by cyber adversaries. The complex and interdependent design of digital systems has the potential to introduce emergent cyber properties that are generally not covered by hazard analyses nor formal nuclear Probabilistic Risk Assessment (PRA). The R&D and supporting analysis presented here explores approaches to predict and manage how interdependent system properties effect risk. To show the potential impact of a successful cyber-attack to formal PRA event tree probabilities, HAZCADS analysis was also used. HAZCADS was also used to model the automatic depressurization system (ADS) automatic actuation. This analysis extended to an integrated system analysis for common-cause failure (CCF). In this aspect, the HAZCADS analysis continued by analyzing plant design details for system connectivity in support of critical plant functions. A dependency matrix was developed to depict the integrated functionality of the interconnected systems. Areas of potential CCF are indicated. Future work could include adversary attack development to show how CCF could be caused, resulting in PRA events. Across the multiple systems that comprise the ECCS, the analysis shows that the change in such probabilities was very different between systems. This indicates that some systems have a larger potential risk impact from successful cyber-attack or digital failure, which indicates a need for these systems to have a higher priority for design and defensive measures. Furthermore, we were able to establish that a risk analysis using any arbitrary threat model establishes an ordering of components with regard to cyber-risk. This ordering can be used to influence the overall system design with an eye to lowering risk, or as a way to understand real-time risk to operational systems based on a current threat landscape. Expert knowledge of both the analysis process and the system being analyzed is required to perform a HAZCADS analysis. The need for a tiered risk analysis is demonstrated by the results of this report.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2023

Uncovering a CF 3 Effect on X‐ray Absorption Energies of [Cu(CF 3 ) 4 ] − and Related Copper Compounds by Using Resonant Diffraction Anomalous Fine Structure (DAFS) Measurements**

Abstract Understanding the electronic structures of high‐valent metal complexes aids the advancement of metal‐catalyzed cross coupling methodologies. A prototypical complex with formally high valency is [Cu(CF 3 ) 4 ] − (1), which has a formal Cu(III) oxidation state but whose physical analysis has led some to a Cu(I) assignment in an inverted ligand field model. Recent examinations of1by X‐ray spectroscopies have led previous authors to contradictory conclusions, motivating the re‐examination of its X‐ray absorption profile here by a complementary method, resonant diffraction anomalous fine structure (DAFS). From analysis of DAFS measurements for a series of seven mononuclear Cu complexes including1, here it is shown that there is a systematic trifluoromethyl effect on X‐ray absorption that blue shifts the resonant Cu K‐edge energy by 2–3 eV per CF 3 , completely accounting for observed changes in DAFS profiles between formally Cu(III) complexes like1and formally Cu(I) complexes like (Ph 3 P) 3 CuCF 3 (3). Thus, in agreement with the inverted ligand field model, the data presented herein imply that1is best described as containing a Cu(I) ion with d n count approaching 10.

Chemistry↗

DOE OSTI2022

Exact WKB and the quantum Seiberg-Witten curve for 4d $N$ = 2 pure SU(3) Yang-Mills. Abelianization

We investigate the exact WKB method for the quantum Seiberg-Witten curve of 4d N = 2 pure SU(3) Yang-Mills in the language of abelianization. The relevant differential equation is a third-order equation on $\mathbb{CP}^1$ with two irregular singularities. We employ the exact WKB method to study the solutions to such a third-order equation and the associated Stokes phenomena. We also investigate the exact quantization condition for a certain spectral problem. Moreover, exact WKB analysis leads us to consider new Darboux coordinates on a moduli space of flat SL(3,$\mathbb{C}$)-connections. In particular, in the weak coupling region we encounter coordinates of the higher length-twist type generalizing Fenchel-Nielsen coordinates. The Darboux coordinates are conjectured to admit asymptotic expansions given by the formal quantum periods series and we perform numerical analysis supporting this conjecture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Interpreting test temperature and loading rate effects on the fracture toughness of polymer-metal interfaces via time–temperature superposition

Here, in this letter, we present interfacial fracture toughness data for a polymer-metal interface where tests were conducted at various test temperatures T and loading rates $\dot{δ}$. An adhesively bonded asymmetric double cantilever beam (ADCB) specimen was utilized to measure toughness. ADCB specimens were created by bonding a thinner, upper adherend to a thicker, lower adherend (both 6061 T6 aluminum) using a thin layer of epoxy adhesive, such that the crack propagated along the interface between the thinner adherend and the epoxy layer. The specimens were tested at T from 25 to 65 °C and $\dot{δ}$ from 0.002 to 0.2 mm/s. The measured interfacial toughness Γ increased as both T and $\dot{δ}$ increased. For an ADCB specimen loaded at a constant $\dot{δ}$, the energy release rate G increases as the crack length a increases. For this reason, we defined rate effects in terms of the rate of change in the energy release rate $\dot{G}$. Although not rigorously correct, a formal application of time–temperature superposition (TTS) analysis to the Γ data provided useful insights on the observed dependencies. In the TTS-shifted data, Γ decreased and then increased for monotonically increasing $\dot{G}$. Thus, the TTS analysis suggests that there is a minimum value of Γ. This minimum value could be used to define a lower bound in Γ when designing critical engineering applications that are subjected to T and $\dot{δ}$ excursions.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Core Design Optimization of the Westinghouse Lead Fast Reactor

Westinghouse is pursuing an advanced Nuclear Power Plant design based on Lead Fast Reactor (LFR) technology for global commercialization. To achieve an optimal combination of key attributes, such as safety, sustainability, and economic competitiveness, Westinghouse and ANL partnered in developing and applying a formalized core design optimization strategy. An LFR analysis workflow was developed to automate a suite of reactor physics, fuels performance, safety, and economics simulations on a selected LFR concept. The workflow streamlines analysis of a wide range of LFR designs with different dimensions and fuel types to assess their viability and economic performance, significantly reducing human processing time and risks of processing errors. The LFR optimization exercise was defined, resulting in selection of the design constraints (geometric, neutronics, thermo-mechanical, safety, thermal-hydraulics, and economics) and performance metrics researched (minimization of both the fuels LCOE and the first core inventory cost). A total of 14 varied design parameters were considered, including assembly dimensions, coolant temperature, and enrichment distribution throughout the core. The LFR analysis workflow was connected to DAKOTA for sensitivity and optimization analyses. Due to the extremely large size of the potential LFR optimization solution space relative to the computing time required to characterize one LFR solution, a multi-stage optimization approach was proposed to breakdown the problem into several stages with more reasonable sizes. This optimization approach enabled finding various viable core solutions with different cost tradeoffs that were considered by Westinghouse and justify selection of a smaller core with multi-batch 2-year cycle length.

Stauff, Nicolas E.↗

DOE OSTI2025

Theorems in Service of Sound Composition, Rapid Modeling and Scalable Analysis

This project extends the state of the art in formal verification modeling with modules and automatically checkable data-sharing patterns such that component modules can retain their assurance case when composed within a larger system. For users, smaller models make reasoning easier and help to ensure they accurately reflect text specifications. For automated methods, smaller models give exponential benefits for verification algorithm execution time.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Geothermal play fairway analysis, part 1: Example from the Snake River Plain, Idaho

The Snake River Plain (SRP) volcanic province overlies the track of the Yellowstone hotspot, a thermal anomaly that extends deep into the mantle. Most of the area is underlain by a basaltic volcanic province that overlies a mid-crustal intrusive complex, which in turn provides the long-term heat flux needed to sustain geothermal systems. Previous studies have identified several known geothermal resource areas within the SRP. For the geothermal study presented herein, our goals were to: (1) adapt the methodology of Play Fairway Analysis (PFA) for geothermal exploration to create a formal basis for its application to geothermal systems, (2) assemble relevant data for the SRP from publicly available and private sources, and (3) build a geothermal PFA model for the SRP and identify the most promising plays, using GIS-based software tools that are standard in the petroleum industry. The study focused on identifying three critical resource parameters for exploitable hydrothermal systems in the SRP: heat source, reservoir and recharge permeability, and cap or seal. Data included in the compilation for heat source were heat flow, distribution and ages of volcanic vents, groundwater temperatures, thermal springs and wells, helium isotope anomalies, and reservoir temperatures estimated using geothermometry. Reservoir and recharge permeability was inferred from the analysis of stress orientations and magnitudes, post-Miocene faults, and subsurface structural lineaments based on magnetics and gravity data. Data for cap or seal included the distribution of impermeable lake sediments and clay-seal associated with hydrothermal alteration below the regional aquifer. These data were used to compile Common Risk Segment maps for heat, permeability, and seal, which were combined to create a Composite Common Risk Segment map for all southern Idaho that reflects the risk associated with geothermal resource exploration and identifies favorable resource tracks. Our regional assessment indicated that undiscovered geothermal resources may be located in several areas of the SRP. Two of these areas, the western SRP and Camas Prairie, were selected for more detailed assessment, during which heat, permeability, and seal were evaluated using newly collected field data and smaller grid parameters to refine the location of potential resources. These higher resolution assessments illustrate the flexibility of our approach over a range of scales.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: $\phi$ 3 QFT in 6 Dimensions

We analyze the asymptotically free massless scalar $\phi$ 3 quantum field theory in 6 dimensions, using resurgent asymptotic analysis to find the trans-series solutions which yield the non-perturbative completion of the divergent perturbative solutions to the Kreimer–Connes Hopf-algebraic Dyson–Schwinger equations for the anomalous dimension. This scalar conformal field theory is asymptotically free and has a real Lipatov instanton. In the Hopf-algebraic approach we find a trans-series having an intricate Borel singularity structure, with three distinct but resonant non-perturbative terms, each repeated in an infinite series. These expansions are in terms of the renormalized coupling. The resonant structure leads to powers of logarithmic terms at higher levels of the trans-series, analogous to logarithmic terms arising from interactions between instantons and anti-instantons, but arising from a purely perturbative formalism rather than from a semi-classical analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Towards a self-consistent analysis of the anisotropic galaxy two- and three-point correlation functions on large scales: application to mock galaxy catalogues

We establish a practical method for the joint analysis of anisotropic galaxy two- and three-point correlation functions (2PCF and 3PCF, respectively) on the basis of the decomposition formalism of the 3PCF using tripolar spherical harmonics. We perform such an analysis with MultiDark-Patchy mock catalogues to demonstrate and understand the benefit of the anisotropic 3PCF. We focus on scales above $80\, h^{-1}\, {\rm Mpc}$, and use information from the shape and the baryon acoustic oscillation (BAO) signals of the 2PCF and 3PCF. We also apply density field reconstruction to increase the signal-to-noise ratio of BAO in the 2PCF measurement, but not in the 3PCF measurement. In particular, we study in detail the constraints on the angular diameter distance and the Hubble parameter. We build a model of the bispectrum or 3PCF that includes the non-linear damping of the BAO signal in redshift space. We carefully account for various uncertainties in our analysis including theoretical models of the 3PCF, window function corrections, biases in estimated parameters from the fiducial values, the number of mock realizations to estimate the covariance matrix, and bin size. The joint analysis of the 2PCF and 3PCF monopole and quadrupole components shows a $30{{\ \rm per\ cent}}$ and $20{{\ \rm per\ cent}}$ improvement in Hubble parameter constraints before and after reconstruction of the 2PCF measurements, respectively, compared to the 2PCF analysis alone. Furthermore, this study clearly shows that the anisotropic 3PCF increases cosmological information from galaxy surveys and encourages further development of the modelling of the 3PCF on smaller scales than we consider.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Kinklike structures in an arcsin real scalar dynamics

Highlights: • Kinklike analyses in a real scalar theory with an arcsin dynamic. • First-order formalism implementation and deformation procedure in an arcsin scalar dynamics. In this paper, we analyze kink-like analytical solutions in a real scalar theory with an arcsin dynamics inspired by the arcsin electrodynamics presented in Kruglov (2015). This analysis is done by means of the first-order formalism. This formalism provides a framework where the equations of motion can be simplified by preserving the linear stability of the theory. In this work, the deformation procedure is implemented with the aim of finding exact solutions in systems with generalized dynamics. Along the paper, we explore how the first-order formalism is implemented in the arcsin kinetics and how such a term influences the kink-like solutions. As a part of the result of our paper, we show that the kink-like solutions are similar to the ones obtained in the standard scalar kinetic theory. We also show that the extra parameter, that controls the non-linearities of the model, plays an essential role in the energy densities and stability potentials. These quantities vary according to this parameter. The goals here are to show how the first-order framework is implemented in this arcsin scenario and to present the analytical kink-like solutions that can be found by means of the first-order framework and deformation method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

From noise to information: The transfer function formalism for uncertainty quantification in reconstructing the nuclear density

The neutron distribution of neutron-rich nuclei provides critical information on the structure of finite nuclei and neutron stars. Parity violating experiments—such as PREX and CREX—provide a clean and largely model-independent determination of neutron densities. Such experiments, however, are challenging and expensive, which is why sound statistical arguments are required to maximize the information gained. We introduce a new framework, the “transfer function formalism,” aimed at uncertainty quantification, model selection, and experimental design in the context of neutron densities. The transfer functions (TFs) are built analytically by expressing the linear response of the objective function (e.g., χ2) to small perturbations of the data. Using the TF formalism, we are able to analyze the expected overall uncertainty—quantified in terms of bias and variance—of the mean square radius and interior density of 48 Ca and 208 Pb. Using relativistic mean field models as a proxy for the weak-charge density—and assuming that a total of five measurements could be performed on the weak form factor of 48 Ca and 208 Pb—we identify the optimal models and experimental locations that minimize the uncertainty in the extraction of the radius and interior density. We also explore the use of the TF formalism to understand the influence of prior distributions for the model parameters, as well as the optimization of model hyperparameters not constrained by the data. Here,we establish how the choice of experimental locations and the model that is used can have a significant impact on the final uncertainties of the extracted quantities of interest. For challenging experiments such as CREX and PREX, a proper quantification of such uncertainties is critical. We have demonstrated how the TF formalism provides several advantages for this type of analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗