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DOE OSTI2026

Improbability of Post-Closure Criticality in Compacted Criticality Control Overpacks after Room Closure at Waste Isolation Pilot Plant

As part of its periodic re-certification of the Waste Isolation Pilot Plant (WIPP), an operating repository in bedded salt for the disposal of transuranic (TRU) waste from atomic energy defense activities, the United States Environmental Protection Agency expects a re-evaluation of features, events, and processes, such as post-closure nuclear criticality. Although salt creep beneficially encapsulates the TRU waste in the closed WIPP repository, the spacing between an array of waste packages is disrupted as the salt creep closes disposal rooms and containers lose structural integrity. For most TRU waste, the possibility of post-closure criticality is exceedingly small either because the salt neutronically isolates TRU waste canisters or because closure of a disposal room from salt creep does not sufficiently compact the low mass of fissile material. The criticality evaluation was updated, however, because of the introduction of criticality control overpack (CCO) containers, which may dispose up to 380 fissile gram equivalent plutonium-239 in each container. The criticality potential is evaluated through high-fidelity geomechanical modeling of a disposal room filled with CCO containers during two representative conditions: (1) large salt block fall, and (2) gradual disposal room closure from salt creep. Geomechanical models of roof fall demonstrate three tiers of CCO containers are not greatly disrupted. Geomechanical models of gradual room closure from salt creep (without brine seepage and subsequent gas generation to permit maximum room closure) were used to predict irregular arrays of closely packed CCOs after 1000 years, when room closure has asymptotically approached maximum compaction. Models of spheres or cylinders with 380 fissile gram equivalent of plutonium (as oxide) at the predicted irregular compacted spacing demonstrate that an array of CCO containers is not critical when surrounded by salt and magnesium oxide, provided the mass of hydrogenous material shipped in CCO containers (usually plastics) is controlled or boron carbide (a neutron poison) is mixed with the fissile contents.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2026

A careful examination of closure models in Euler–Lagrange Simulations of compressible multiphase flow in a planar shock particle curtain problem

In this work we present a comprehensive investigation of state-of-the-art closure models employed to represent interphase momentum, thermal, and work exchange between the gas and particulate phases for Euler–Lagrange (EL) simulations in shock-driven flows. A complete list of closures for the force, torque, heat transfer, and work exchange models is provided. In particular, the present work includes a stochastic closure for the particle-to-particle variation in the quasi-steady force and a deterministic closure for particle-to-particle variation in the added mass force in an EL framework. These variations arise due to the presence of neighboring particles and particle–particle interactions. To investigate the importance of each closure term, we carry out fully three-dimensional simulations for a planar shock propagating over a random bed of inert particles. The primary goal is to evaluate the role of each closure term on the gas dynamic features (such as transmitted and reflected shock locations) and particle curtain features (such as upstream and downstream curtain locations). To this end, thirteen cases are considered, with each case progressively including a closure model with the goal to identify and quantify its contribution to the simulated dynamics. We show that the volume fraction dependence of the mean force models plays an important role in generating wave-like instabilities that lead to concentration bands. In addition, fluctuations in quasi-steady and added mass forces primarily decrease the internal instabilities that tend to enhance local volume fraction variations. Particle rotation is primarily due to inter-particle collisions, is generally weak, and does not play an important role in the translational dynamics for the present configuration. Inter-phase heat transfer has a strong effect on gas phase temperature, slows down the transmitted and reflected shocks, and decreases the width of the curtain. Furthermore, the absence of a work-coupling model fails to conserve the total energy, greatly under-predicts the gas temperature which in turn affects the particle dynamics.

Compressible flow↗

DOE OSTI2026

Improbability of Post-Closure Criticality in Array of Transuranic Waste Containers after Compaction by Salt Creep at Waste Isolation Pilot Plant

Based on the rationale presented, post-closure nuclear criticality is improbable when room closure compacts containers disposing transuranic (TRU) waste emplaced at the Waste Isolation Pilot Plant (WIPP), an operating repository in bedded salt in southeastern New Mexico. As described in the original WIPP certification, a qualitative estimate of the probability of post-closure criticality in TRU waste produced from atomic energy defense activities has been low either because remote-handled TRU waste canisters are neutronically isolated by the bedded salt or because the low fissile mass in an array of contact-handled TRU waste drums cannot be compacted sufficiently by room closure from salt creep. These situations are still valid for the majority of TRU waste that is disposed at WIPP without any disposal constraints, as updated herein. This report also qualitatively evaluates the probability of criticality after disposal of TRU waste in pipe overpack containers (POC) where every POC in a shipment may have the maximum 200 fissile gram equivalent of 239Pu content. The probability of criticality for a disposal room filled with POCs is estimated during four representative phases of repository evolution: (1) a large salt block falls onto POCs in the first 20 years, (2) salt creep closes a disposal room in the first 1000 years without brine seepage and subsequent gas generation, which permits maximum compaction, (3) some brine seepage occurs into the closed room, which initiates consumption of the fiberboard (cellulose) impact absorber in the POC in the second 1000 years, and (4) full brine inundation of a room and consumption of all fiberboard thereafter. Salt-block fall in the first phase does not greatly disrupt three tiers of POCs. The compacted spacing of POCs in the later three repository conditions is calculated through high-fidelity, geomechanical modeling. Criticality evaluation of compacted 200-g 239 Pu spheres at the compacted spacing shows that neither 12-inch nor 6-inch POCs are critical after the first 1000 years, the second 1000 years, or thereafter as the sea of reflector material changes to represent the three repository conditions. Specifically, fiberboard and iron isolates 239 Pu while dry, and brine reduces the reactivity when a room is partially and fully inundated. Because POC behavior bounds behavior of other standard TRU waste containers, post-closure criticality caused by room closure compacting containers is omitted in the performance assessments for the 2019 and 2026 WIPP compliance re-certification applications to the US Environmental Protection Agency.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2026

Second Order Closures for the Radiative Transfer Equation: Some Are Unstable

The largest existing simulations of cosmic reionization model radiative transfer with moment methods that require a closure relation. The two most commonly used closure relations are M1 and OTVET; both close the moment hierarchy at the first moment. We explore the properties of a higher, second-order closure. We show that direct generalizations of M1 and OTVET to one higher order are physically unstable - i.e., the closure equations themselves result in unstable solutions, not just their numerical implementation. In fact, a generalization of OTVET to any order higher than the first one is unstable. We are also able to show that any local (i.e., depending only on the local moments of the radiation field, like M1) second-order closure that depends only on the radiation intensity and radiation flux, but does not explicitly depend on the radiation pressure, is physically unstable. This result restricts the choice of possible second-order closure relations.

Gnedin, Nickolay Y. [Fermilab; Chicago U., Astron.↗

DOE OSTI2025

Structure-preserving neural networks for the regularized entropy-based closure of a linear, kinetic, radiative transport equation

The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural network-based approximation to the entropy-based closure method to accurately compute the solution of the multi-dimensional moment system with a low memory footprint and competitive computational time. We extend methods developed for the standard entropy-based closure to the regularized entropy-based closures. The main idea is to interpret structure-preserving neural network approximations of the regularized entropy-based closure as a two-stage approximation to the original entropy-based closure. We conduct a numerical analysis of this approximation and investigate optimal parameter choices. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive computation times and simulation accuracy. The code and all trained networks are provided on GitHub.

entropy closure↗

DOE OSTI2025

Flux-Closure Domain Structures in Ferroelectric K 0.5 Na 0.5 NbO 3 Thin Films

Topological domain structures in ferroelectric materials have garnered increasing attention due to their intriguing physical properties and promising applications. While most existing topological structures in ferroelectric perovskite oxides originate from tetragonal or rhombohedral bulk phases, much less is understood about their counterparts in orthorhombic ferroelectrics. Here, in this work, we employ ferroelectric K 0.5 Na 0.5 NbO 3 (KNN) thin films as a model system and leverage phase-field simulations to theoretically predict the static structures and dynamic behaviors of three types of flux-closure domain configurations: in-plane (Type-I), out-of-plane (Type-II), and superdomain (Type-III) flux-closure structures. We systematically investigate the effects of finite size, misfit strains, and electrical boundary conditions on the formation and switching of these topological structures. For the Type-I structure, size reduction or small misfit strain facilitates a transition of the flux-closure pattern to polar vortices. Type-II structures emerge under open-circuit electrical boundary conditions of the film, forming at the junctions of specific domain walls with the film surface or the film–substrate interface. The formation mechanisms of these two flux-closure structures are rationalized from an energy perspective. We demonstrated switching capabilities of Type-II and Type-III structures by obtaining polarization–electric field hysteresis loops. Our simulations also reveal a reversible electric-field-induced transition between the orthorhombic and rhombohedral ferroelectric phases with a checkerboard domain pattern, during which the integrity of the flux-closure structure is preserved. These findings provide theoretical insights and practical guidance for identifying and manipulating topological structures in low-symmetry ferroelectrics, paving the way for developing energy-efficient microelectronic devices based on topological structures.

P-E loop↗

DOE OSTI2025

Implications of a weakening N = 126 shell closure away from stability for r -process astrophysical conditions

The formation of the third r-process abundance peak near A ∼ 195 is highly sensitive to both nuclear structure far from stability and the astrophysical conditions that produce the heaviest elements. In particular, the N = 126 shell closure plays a crucial role in shaping this peak. Experimental data hints that the shell weakens as proton number departs from Z = 82, a trend largely missed by global mass models. To investigate its impact on r-process nucleosynthesis, we employ both standard global models with strong closures and modified Duflo-Zuker (DZ) models that reproduce the weakening, combined with three sets of β − -decay rates. Strong shell closures generate sharply peaked abundances, whereas weakened closures consistent with the experimental trend produce broader, flatter patterns. Accurately reproducing the solar third peak under weakened shell strength requires sufficiently neutron-rich conditions that significant fission occurs, and slower decay rates. These results demonstrate that a weakening N = 126 shell closure away from stability imposes significant constraints on the astrophysical environments of the r-process and underscores the need for precise mass measurements and improved characterization of β − -decay properties in this region.

N = 126 closed shells↗

DOE OSTI2025

Quantum maximum entropy closure for small flavor coherence

Quantum angular moment transport schemes are an important avenue toward describing neutrino flavor mixing phenomena in dense astrophysical environments such as supernovae and merging neutron stars. Successful implementation will require new closure relations that go beyond those used in classical transport. In this paper, we derive the first analytic expression for a quantum M1 closure, valid in the limit of small flavor coherence, based on the maximum entropy principle. We verify that the resulting closure relation has the appropriate limits and characteristic speeds in the diffusive and free-streaming regimes. We then use this new closure in a moment linear stability analysis to search for fast flavor instabilities in a binary neutron star merger simulation and find better results as compared with previously designed, ad hoc , semiclassical closures.

astrophysical & cosmological simulations↗

DOE OSTI2025

Quantum closures for neutrino moment transport

A computationally efficient method for calculating the transport of neutrino flavor in simulations is to use angular moments of the neutrino one-body reduced density matrix, i.e., “quantum moments.” As with any moment-based radiation transport method, a closure is needed if the infinite tower of moment evolution equations is truncated. We derive a general parametrization of a quantum closure and the limits the parameters must satisfy in order for the closure to be physical. We then derive from multiangle calculations the evolution of the closure parameters in two test cases which we then progressively insert into a moment evolution code and show how the parameters affect the moment results until the full multiangle results are reproduced. This parametrization paves the way to setting prescriptions for genuine quantum closures adapted to neutrino transport in a range of situations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Quantum mechanical closure of partial differential equations with symmetries

We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a quantum mechanical representation, we use the space of quantum density operators to model the unresolved degrees of freedom of the original dynamics in a statistical sense, and the framework of quantum measurement to predict their contributions to the resolved dynamics. The embedded dynamics is discretized by a positivity preserving process, leading to a compressed representation that is invariant under the dynamical symmetries of the resolved dynamics. We present a data based formulation of the closure scheme and apply it to a closure problem for the shallow water equations. The numerical results demonstrate that our closure model can accurately predict the main features of the true dynamics, including for out of sample initial conditions.

Delay embedding↗

DOE OSTI2025

Machine learning for reparameterization of multi-scale closures

Scientific machine learning (ML) is becoming increasingly useful in learning closure models for multi-scale physics problems; however, many ML approaches require a vast array of training data and can struggle with generalization and interpretability. Here, rather than learning an entire closure operator, we adopt an existing reduced-dimension model of the microphysics and learn an optimal re-parameterization of the solver. We demonstrate two approaches for training the reduced dimension closure model (1) an a priori method that optimizes the closure parameterization and the neural network parameters separately and (2) an a posteriori method that simultaneously optimizes both. Using the simulation of biomass pyrolysis as a motivating example, we show that the a posteriori method achieves better target losses and is less dependent on training dataset size for generalizability. We then demonstrate the impact that implementing this reparameterization has at the macroscale, showing improved predictive performance with no modification to the underlying macroscale solvers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Closure Report for Corrective Action Unit 116: Area 25 Test Cell C Facility, Nevada National Security Site, Nevada with ROTC-1

CR loaded to this OSTI record. Just adding new file which includes CR plus new ROTC 1 and update the metadata to the following: This Closure Report (CR) presents information supporting closure of Corrective Action Unit (CAU) 116, Area 25 Test Cell C Facility. This CR complies with the requirements of the Federal Facility Agreement and Consent Order (FFACO) that was agreed to by the State of Nevada; the U.S. Department of Energy (DOE), Environmental Management; the U.S. Department of Defense; and DOE, Legacy Management (FFACO, 1996 [as amended March 2010]). CAU 116 consists of the following two Corrective Action Sites (CASs), located in Area 25 of the Nevada National Security Site: (1) CAS 25-23-20, Nuclear Furnace Piping and (2) CAS 25-41-05, Test Cell C Facility. CAS 25-41-05 consisted of Building 3210 and the attached concrete shield wall. CAS 25-23-20 consisted of the nuclear furnace piping and tanks. Closure activities began in January 2007 and were completed in August 2011. Activities were conducted according to Revision 1 of the Streamlined Approach for Environmental Restoration Plan for CAU 116 (U.S. Department of Energy, National Nuclear Security Administration Nevada Site Office [NNSA/NSO], 2008). This CR provides documentation supporting the completed corrective actions and provides data confirming that closure objectives for CAU 116 were met. Site characterization data and process knowledge indicated that surface areas were radiologically contaminated above release limits and that regulated and/or hazardous wastes were present in the facility. The Record of Technical Change 1 updated the use restriction information.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Ethical considerations in infectious disease modelling for public health policy: the case of school closures

Mathematical models of infectious diseases are frequently used as a tool to support public health policy and decisions around the implementation of interventions such as school closures. However, most publications on policy-relevant modelling lack an ethical framework and do not explicitly consider the ethical implications of the work. This creates a risk that the unintended consequences of interventions are overlooked or that models are used to justify decisions that are inconsistent with public health ethics. In this article, we focus on the case study of school closures as a commonly modelled intervention against pandemic influenza, COVID-19 and other infectious disease threats. We briefly review some of the key concepts in public health ethics and describe approaches to modelling the effects of school closures. We then identify a series of ethical considerations involved in modelling school closures. These include accounting for population heterogeneity and inequalities; including a diversity of viewpoints and expertise in model design; considering the distribution of benefits and harms; and model transparency and contextualization. Furthermore, we conclude with some recommendations to ensure that policy-relevant modelling is consistent with some key ethics values.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Explosively Formed Helical Closure for Radioactive Material Packaging

Benefits • Allows for the creation of features in thin-walled metal parts that would otherwise be impossible or impractical to create. • Reduces margin of error during radioactive material package closure. • Increases efficiency of package closure and opening. Applications and Industries • The tooling and method could be used to create closures for any industrial application. There may be use for the geometry produced by the tooling and method that is outside of closures.

Timmons, Darren↗

DOE OSTI2025

Development of a Helical Closure for Radioactive Material Shipping Packages

The Savannah River National Laboratory (SRNL) Packaging Technology group proposed a closure design for the outer packaging of a prototype Type B shipping package being developed for the Department of Energy (DOE). The closure design provides an efficient means of securing the containment vessel (CV) within the radioactive material packaging. This design has a simplified operation, requires less components, and less maintenance when compared to current radioactive material package closure methods. This paper will review and discuss the materials, designs, processes, and testing activities that were considered and pursued in the development of the novel closure for the outer packaging of new radioactive material shipping packages.

Housley, William M. [Savannah River National Labor↗

DOE OSTI2025

Closure and transport theory for plasmas with multiple ion species

This report summarizes a DOE-funded research project on closure and transport theory for plasmas with multiple ion species. The work developed accurate moment-based closure models across the full range of collisionality, incorporating both kinetic and collisional effects. Key contributions include high-fidelity closure relations, multi-temperature models, and transport coefficients applicable to fusion, space, and astrophysical plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Closure Report for Corrective Action Unit 366: Area 11 Plutonium Valley Dispersion Sites, Nevada National Security Site, Nevada with ROTC 1

This Closure Report presents information supporting closure of Corrective Action Unit (CAU) 366, Area 11 Plutonium Valley Dispersion Sites, and provides documentation supporting the completed corrective actions and confirmation that closure objectives for CAU 366 were met. CAU 366 consists of the following six Corrective Action Sites (CASs), located in Area 11 of the Nevada National Security Site: • CAS 11-08-01, Contaminated Waste Dump #1 • CAS 11-08-02, Contaminated Waste Dump #2 • CAS 11-23-01, Radioactively Contaminated Area A • CAS 11-23-02, Radioactively Contaminated Area B • CAS 11-23-03, Radioactively Contaminated Area C • CAS 11-23-04, Radioactively Contaminated Area D

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Modeling hydraulic fracture opening and closure with proppant transport and settlement

Hydraulic fracturing is a widely used reservoir stimulation technique for improving fluid circulation in rock formations with extremely low permeability, particularly in enhanced geothermal systems (EGS). To better understand the complex processes involved and improve hydraulic stimulation performance, we have developed ELK (ELectrical fracKing), a MOOSE-based 3D finite element application designed to model the behavior of proppant-fluid mixtures in propagating fractures. ELK integrates both the fluid and proppant components, incorporating particle-driven processes such as gravity settling, particle-particle interactions, and strong density and viscosity contracts, in addition to conventional fluid-driven fracture propagation. In this contribution, we extend ELK to model propped fracture closure, which occurs after the injection phase due to a dramatic drop in the effective stress on the fracture plane. During the shut-in, flowback, and production periods, the fracture width decreases, with the closure behavior depending on proppant concentration.. At low concentrations, closure follows a nonlinear joint law linked to the stiffness of asperities in the fracture walls. While at high concentrations, it is controlled by the properties of packed proppant bed. The extended ELK application is validated against several benchmark examples, including the propagation of an inclined frictional crack, fracture opening and sliding in response to fluid injection, and flowback analysis. We believe that ELK’s enhanced capabilities can serve as a valuable tool for the design and optimization of EGS deployment.

15 - GEOTHERMAL ENERGY↗