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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12

Nonlinear optical diode effect in a magnetic Weyl semimetal

Diode effects are of great interest for both fundamental physics and modern technologies. Electrical diode effects (nonreciprocal transport) have been observed in Weyl systems. Optical diode effects arising from the Weyl fermions have been theoretically considered but not probed experimentally. Here, we report the observation of a nonlinear optical diode effect (NODE) in the magnetic Weyl semimetal CeAlSi, where the magnetization introduces a pronounced directionality in the nonlinear optical second-harmonic generation (SHG). We demonstrate a six-fold change of the measured SHG intensity between opposite propagation directions over a bandwidth exceeding 250 meV. Supported by density-functional theory, we establish the linearly dispersive bands emerging from Weyl nodes as the origin of this broadband effect. We further demonstrate current-induced magnetization switching and thus electrical control of the NODE. Our results advance ongoing research to identify novel nonlinear optical/transport phenomena in magnetic topological materials and further opens new pathways for the unidirectional manipulation of light.

36 MATERIALS SCIENCE↗

Non-volatile electric control of antiferromagnetic states on nanosecond timescales

Electrical manipulation of antiferromagnetic (AFM) states, a cornerstone of AFM spintronics, is a great challenge, requiring novel material platforms. Here we report the full control over AFM states by voltage pulses in the insulating Co 3 O 4 spinel well below its Néel temperature. We show that the strong linear magnetoelectric effect is fully governed by the orientation of the Néel vector. As a unique feature of Co 3 O 4 , the magnetoelectric energy can easily overcome the weak magnetocrystalline anisotropy, thus, the N´eel vector can be manipulated on demand, either rotated smoothly or reversed suddenly, by combined electric and magnetic fields. We achieve the non-volatile switching within a few tens of nanoseconds between time-reversed AFM states in macroscopic volumes by voltage pulses. These observations render quasi-cubic antiferromagnets, like Co 3 O 4 , an ideal platform for the ultrafast (pico- to nanosecond) manipulation of microscopic AFM domains and may pave the way for the realization of AFM spintronic devices.

36 MATERIALS SCIENCE↗

A practical control strategy for demand flexibility with ensured occupant comfort in grid-interactive efficient buildings

This study proposes a practical and simplified demand response (DR) control strategy from the perspective of grid-interactive efficient buildings (GEBs), aiming to secure demand flexibility while ensuring occupant thermal comfort. Focusing on summer on-peak periods, a linear demand response (LDR) strategy that integrates cooling setpoint adjustment and lighting dimming was designed, and its performance was quantitatively evaluated. A case study was conducted using EnergyPlus-based simulations for a U.S. DOE small office prototype building under summer on-peak weather conditions. Compared with a conventional rapid demand response (RDR) strategy, the proposed LDR approach gradually reduced electrical loads while maintaining occupant thermal comfort indices, including predicted mean vote (PMV) and predicted percentage of dissatisfied (PPD), within acceptable comfort ranges. Quantitative analysis of demand flexibility using the grid-interactive impact index (GII) and the flexibility strength index (FSI) showed that the LDR strategy provided approximately 12.5% demand flexibility during DR periods and achieved an electricity cost reduction of about 8.8%. In addition, the results of the part-load ratio (PLR)-based cooling system performance analysis showed that, in the on-peak period, the LDR strategy exhibited improved cooling performance compared with the baseline. Overall, this study shows the potential of a practical DR control strategy that can simultaneously achieve occupant comfort and demand flexibility without relying on complex advanced control technologies.

Jung, Dong Eun↗

A Hybrid Fuel Cell and Battery Storage Power Management for Grid-Interactive EV Charging Station

With the increasing adoption of renewable energy sources in grid-interactive Electric Vehicle (EV) charging stations, the role of energy storage systems has become critical. While large energy storage systems have mitigated the intermittency of renewable energy, integrating multi-source energy management with prioritized charging can further enhance the reliability of charging stations (CS). This paper presents a decentralized energy management (DEM) approach combining battery energy storage (BES) and fuel cell (FC) systems using a rule-based line resistance correction droop (LRCD) control technique. The proposed droop control dynamically adjusts the gain to balance the state-of-charge (SoC) of the BES, enhancing power support longevity and improving battery life under varying capacity conditions by reducing current stress. Additionally, the paper addresses the challenges of using fuel cells in linear regions to optimize efficiency and manage various charging scenarios. The CS integrates unity power factor grid interaction, and power support for auxiliary loads, maintaining harmonic distortion within 5% during grid islanding. The approach evaluates DC bus voltage regulation under various scenarios of PV array power fluctuations and dynamic load variations, in both grid-connected and standalone operations. In conclusion, the proposed control strategy is validated on a laboratory prototype through various dynamic load variation and grid islanding scenarios.

Khalid, Mohd [Oak Ridge National Laboratory (ORNL)↗

Investigating the FLASH Effect in a Rat Brain Organotypic Model With a Novel High-Energy Electron Beam

Ultrahigh dose rate (FLASH) radiation therapy is reported to reduce normal tissue toxicity while maintaining tumor control; however, mechanism(s) remain obscure. To study FLASH mechanisms in brain tissue, we developed a novel experimental platform featuring a specialized high-energy electron linear accelerator, High Intensity Gamma Ray Source (HIGS), paired with an organotypic ex vivo brain metastasis model. We varied interpulse spacing to modulate the mean dose rate (MDR) of our unique 35 MeV electron beam, while maintaining extremely high instantaneous dose rate (IDR). We characterized dosimetry and targeting accuracy of the FLASH beam with film dosimetry. We combined this FLASH beam with an organotypic rat brain slice/breast carcinoma coculture model of brain metastasis to assess effects on normal and neoplastic tissues. Live-cell and bioluminescence imaging demonstrated cancer cell growth effects, whereas normal tissue responses and immune activation were assessed using live-cell imaging, cytokine profiles, and confocal microscopy. Here, we performed comparison experiments with 20 MeV electrons from a Varian clinical linear accelerator (VCLA) using conventional dose rates. The highest IDR of the FLASH beam to date was 20.7 ± 0.6 MGy/s, with maximum MDR of 20.7 MGy/s delivered in 1 pulse of 1 µs duration. Beam targeting was accurate to <1 mm and reproducible. HIGS-FLASH and VCLA dose rates equivalently decreased cancer cell growth. HIGS-FLASH irradiation significantly increased tumor necrosis factor α and fractalkine levels and confocal microscopy revealed distinct changes in microglial morphology slices suggesting microglia activation. Our novel experimental platform produces extremely high dose rates and rapid normal/neoplastic tissue readouts for mechanistic research into the effects of FLASH radiation in the brain. HIGS-FLASH irradiation induces comparable cancer cell growth inhibition but differential effects on cytokines and microglial morphology, suggesting that acute innate immune responses may be involved in FLASH normal tissue effects in the brain.

Kay, Tyler V. [Duke University, Durham, NC (United↗

Design and Materials of Reference Electrodes for Radioactive Waste Tank Service – A Literature Review

The Hanford site stores approximately 55 million gallons of radioactive and chemically hazardous wastes from the production of weapons materials. The wastes are stored in 177 underground, carbon steel storage tanks, 149 of these are single shell tanks (SSTs) and 28 of these are double shell tanks (DSTs). The DSTs provide critical retrieval and interim storage before the waste is vitrified in the Waste Treatment and Isolation Plant (WTP). The DSTs have been in service for 38 to 56 years and current plans indicate that WTP operations will be completed in 2075. Thus, the tanks will need to remain in service far beyond the initial 40-year life expectancy. For life extension of the tanks, effective corrosion control practices must remain in force. This effort includes direct measurements of the extent of corrosion (e.g., ultrasonic measurements and corrosion coupons) and electrochemical processes (e.g., linear polarization measurements).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Initial Uncertainty Analysis of Carbon Tetrachloride Contamination and Remediation in the Ringold A and Lower Mud Units at the Central Plateau

The long-term effectiveness of groundwater cleanup at the Hanford Site Central Plateau depends on predictive models that can capture key uncertainties in contaminant fate and transport. Carbon tetrachloride (CCl 4 ), a persistent and toxic compound, presents particular challenges due to variability in degradation rates, uncertainty in initial plume distribution, and subsurface heterogeneity. These uncertainties directly influence plume persistence, migration pathways, and remedy performance, and thus must be systematically evaluated to support long-term remediation planning. To address these gaps, a large-scale Monte Carlo analysis was conducted using the Plateau to River (P2R) model framework. The modeling approach parameterized three primary uncertainty factors: (1) degradation rate, (2) initial plume distribution, and (3) hydraulic conductivity. Degradation was represented as a first-order process, with half-lives ranging from 70 to 700 years. Initial plume distributions were created using a geostatistical simulation method (sgsim), which generates many equally plausible versions of how contaminants might be distributed underground. From this, 100 different scenarios were mapped onto the P2R grid. Variability in hydraulic conductivity was represented in a similar way, with 100 scenarios each for the Ringold Lower Mud and Ringold A units (layers 6 and 7), based on fitted exponential variograms and conditioned to well data. In total, more than 1000 realizations were simulated to assess plume behavior under uncertainty. Results demonstrate that degradation kinetics exert the strongest control over plume persistence: Shorter half-lives produced rapid mass reduction, while longer half-lives yielded persistent plumes with limited attenuation. A nonlinear response was observed, with steep mass reductions at half-lives greater than 200 years and near-linear declines beyond this threshold, reflecting interactions between degradation and pumping. The initial plume distribution strongly influenced early transport patterns, with broader sources generating larger plume footprints, although pump-and-treat operations constrained plume migration to managed areas. By comparison, hydraulic conductivity variability in the Ringold units had only a secondary influence, modifying spreading behavior without altering the dominant migration pathways governed by source configuration and hydraulic controls. Overall, the analysis highlights that uncertainty in degradation rate and initial plume configuration are the primary drivers of variability in plume predictions, while conductivity heterogeneity plays a limited role. These findings underscore the need for improved site-specific data on degradation processes and source characterization to enhance the reliability of long-term performance assessments and to better inform remedial decision-making at the Central Plateau.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Analysis of a Heat Balance Experiment in the TREAT Reactor with SPARTA and OpenMC

This article presents the interpretation of a heat balance experiment in TREAT using the SPARTA methodology and an OpenMC model. The study examines the effects of control rods and temperature variations on the effective multiplication factor ($k_{\rm eff}$) and correction factors. Results indicate that both core temperature and rod positions have a linear effect on $k_{\rm eff}$ and correction factors in the upper-west channel. A critical hypothesis of SPARTA was validated: reactivities and correction factors can be obtained by linearly combining individual effects. The previously considered negligible effect of temperature on correction factors was found to be significant, necessitating updates to the SPARTA methodology. By fitting an exponential curve to mean temperature data, SPARTA's accuracy and convergence have been improved. Comparisons between SPARTA and OpenMC showed consistent reactivity removal due to temperature increase. While SPARTA effectively interprets complex transients, simpler methods may suffice when correction factors have minimal influence on reactivity calculations.

73 - NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Modeling the effect of wind speed and direction shear on utility‐scale wind turbine power production

Abstract Wind speed and direction variations across the rotor affect power production. As utility‐scale turbines extend higher into the atmospheric boundary layer (ABL) with larger rotor diameters and hub heights, they increasingly encounter more complex wind speed and direction variations. We assess three models for power production that account for wind speed and direction shear. Two are based on actuator disc representations, and the third is a blade element representation. We also evaluate the predictions from a standard power curve model that has no knowledge of wind shear. The predictions from each model, driven by wind profile measurements from a profiling LiDAR, are compared to concurrent power measurements from an adjacent utility‐scale wind turbine. In the field measurements of the utility‐scale turbine, discrete combinations of speed and direction shear induce changes in power production of −19% to +34% relative to the turbine power curve for a given hub height wind speed. Positive speed shear generally corresponds to over‐performance and increasing magnitudes of direction shear to greater under‐performance, relative to the power curve. Overall, the blade element model produces both higher correlation and lower error relative to the other models, but its quantitative accuracy depends on induction and controller sub‐models. To further assess the influence of complex, non‐monotonic wind profiles, we also drive the models with best‐fit power law wind speed profiles and linear wind direction profiles. These idealized inputs produce qualitative and quantitative differences in power predictions from each model, demonstrating that time‐varying, non‐monotonic wind shear affects wind power production.

Energy & Fuels↗

Four-dimensional phase-space reconstruction of flat and magnetized beams using neural networks and differentiable simulations

Beams with cross-plane coupling or extreme asymmetries between the two transverse phase spaces are often encountered in particle accelerators. Flat beams with large transverse-emittance ratios are critical for future linear colliders. Similarly, magnetized beams with significant cross-plane coupling are expected to enhance the performance of electron cooling in hadron beams. Preparing these beams requires precise control and characterization of the four-dimensional transverse phase space. In this study, we employ generative phase-space reconstruction techniques to rapidly characterize magnetized and flat-beam phase-space distributions using a conventional quadrupole-scan method. The reconstruction technique is experimentally demonstrated on an electron beam produced at the Argonne Wakefield Accelerator and successfully benchmarked against conventional diagnostics techniques. Specifically, we show that predicted beam parameters from the reconstructed phase-space distributions (e.g., as magnetization and flat-beam emittances) are in excellent agreement with those measured from the conventional diagnostic methods. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

Phase-field model of freeze casting

Directional solidification of water-based solutions has emerged as a versatile technique for templating hierarchical porous materials. However, the underlying mechanisms of pattern formation remain incompletely understood. In this work, we present a detailed derivation and analysis of a quantitative phase-field model for simulating this nonequilibrium process. The phase-field model extends the thin-interface formulation of dilute binary alloy solidification with antitrapping to incorporate the highly anisotropic energetic and kinetic properties of the partially faceted ice-water interface. This interface is faceted in the basal plane normal to the ⟨0001⟩ directions and atomically rough in other directions within the basal plane. On the basal plane, the model reproduces a linear or nonlinear relationship between the interface growth rate and the kinetic undercooling that can be linked to experimental measurements. In both cases, spontaneous parity breaking of the solidification front is observed when the preferred growth direction is aligned with the temperature gradient. This phenomenon leads to the formation of partially faceted ice lamellae that drift laterally in one of the ⟨0001⟩ directions. Here, we demonstrate that the drifting velocity of the ice lamellae is controlled by the kinetics on the basal plane and converges as the thickness of the diffuse solid-liquid interface decreases. Furthermore, we examine the effect of the form of the kinetic anisotropy, which is chosen here such that the inverse of the kinetic coefficient varies linearly from a finite value in the ⟨0001⟩ directions to zero in all other directions within the basal plane, consistent with the assumption that the interface grows in local thermodynamic equilibrium in this plane. Our results indicate that the drifting velocity of ice lamellae is not affected by the slope of this linear relation, and the radius and undercooling at the tip of an ice lamella converge at relatively small slope values. Consequently, the phase-field simulations remain quantitative with computationally tractable choices of both the interface thickness and the slope assumed in the form of the kinetic anisotropy.

Materials science↗

Regional surrogates for predictive control of digital twins

Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.

Data-driven model↗

Non-linear MHD modelling of transients in tokamaks: a review of recent advances with the JOREK code

Transient magneto-hydrodynamic (MHD) events like edge localized modes (ELMs) or disruptions are a concern for magnetic confinement fusion power plants. Research with the MHD code JOREK towards understanding control of such instabilities is reviewed here in a concise way to provide a complete overview, while we refer to the original publications for details. Experimental validation for unmitigated vertical displacement events progressed. The mechanism of vertical force mitigation by impurity injection was identified. Two-way eddy current coupling to CARIDDI was completed. Shattered pellet injection was simulated in JET, KSTAR, ASDEX Upgrade (AUG) and ITER. Benign runaway electron beam termination in JET and ITER was studied. Coupling of kinetic REs to the MHD is ongoing and a virtual RE synchrotron radiation diagnostic was developed. Regarding pedestal physics, regimes devoid of large ELMs in AUG were simulated and predictive JT60-SA simulations are ongoing. For ELM suppression by resonant magnetic perturbations (RMPs), AUG, ITER and EAST simulations were performed. A free boundary RMP model was validated against experiments. Evidence for penetrated magnetic islands at the pedestal top based on AUG experiments and simulations was found. Simulations of the naturally ELM-free quiescent H-mode in AUG and HL-3 show external kink mode formation prevents pedestal build-up towards an ELM within windows of the edge safety factor. With kinetic neutral particles, high field side high density formation in ITER was simulated and with kinetic impurities, tungsten transport in AUG RMP plasmas was studied. To capture turbulent transport, electro-static full-f particle in cell models for ion temperature gradient and trapped electron modes were established and benchmarked. Application to RMP plasmas shows enhanced turbulence in comparison to unperturbed states. Energetic particle interactions with MHD were studied. Flux pumping that prevents the safety factor on axis from dropping below unity was simulated. First non-linear stellarator applications include current relaxation in $l$ = 2 stellarators, while verification for advanced stellarators progresses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Improving photovoltaic hosting capacity of distribution networks with coordinated inverter control: A case study of the EPRI J1 feeder

Abstract Adding photovoltaic (PV) systems in distribution networks, while desirable for reducing the carbon footprint, can lead to voltage violations under high solar‐low load conditions. The inability of traditional volt‐VAr control in eliminating all the violations is also well‐known. This article presents a novel coordinated inverter control methodology that leverages system‐wide situational awareness to significantly improve hosting capacity (HC). The methodology employs a real‐time voltage‐reactive power (VQ) sensitivity matrix in an iterative linear optimizer to calculate the minimum reactive power intervention from PV inverters needed for mitigating over‐voltage without resorting to active power curtailing or requiring step voltage regulator setting changes. The algorithm is validated using the EPRI J1 feeder under an extensive set of realistic use cases and is shown to provide 3x improvement in HC under all scenarios.

Dalal, Dhaval [School of Electrical, Computer, and↗

Dual-polarization O-band silicon photonics transmitter with an integrated tunable laser, Mach-Zehnder modulators, and SOAs

Presented is an O-band silicon photonics dual-polarization coherent/IMDD modulator integrated with semiconductor optical amplifiers and tunable laser to enhance the short-reach link budget. The laser demonstrated output power >6 dBm and a <250 kHz linewidth over a 14 nm tuning range. Modulators paired with custom 64 Gbaud QPSK drivers exhibited improved analog link sensitivity compared to similar devices without integrated gain sections. They also demonstrated 53 Gbaud dual-polarization PAM4 operation when characterized with a linear driver and MaxLinear 100G/lane DSP board. Both optical links achieved BERs at the KP4-FEC threshold and overall transmitter assembly energy consumption <6.9 pJ/bit without any thermal control when at steady room temperatures.

Liu, Junqian (ORCID:0000000167337650)↗

Development of a Robust Reference Electrode in Aggressive Chemical and Radiation Environments in the Hanford Waste Tanks

The Hanford site stores more than 200 million liters of radioactive and chemically hazardous wastes from the production of weapons materials. The wastes are stored in 177 underground carbon-steel storage tanks, separated between 149 single shell tanks (SSTs) and 28 double shell tanks (DSTs). The DSTs provide critical retrieval and interim storage before the waste is vitrified in the Waste Treatment and Isolation Plant (WTP). The tanks will need to remain in-service far beyond the initial 40-year design life, and effective corrosion control practices must remain in force to extend the tanks’ lifespans. This effort includes direct measurements of corrosion rate (e.g., ultrasonic measurements and corrosion coupons) and electrochemical processes (e.g., linear polarization measurements and open circuit potential measurements). The Hanford site began monitoring the corrosion potential in select DSTs in 2008. Of the 45 reference electrodes that have been installed, 29 have failed and 6 others provided unreliable results. DOE-EM is supporting a 3-year program to develop a chemical and radiation resistant reference electrode for application in the Hanford tanks. The first year of the program focused on understanding the failure mechanism for the reference electrodes and identification of candidate construction materials that would mitigate degradation of the electrodes in the waste environment. During the second year of the program, the objectives were to: 1) test candidate materials under simulated waste conditions, 2) design components that will extend the service life of the electrode, 3) fabricate materials for prototype reference electrodes, and 4) assemble prototype reference electrodes for accelerated testing. The reference electrode is constructed of four principal parts: 1) junction, 2) casing, 3) inner chamber backfill materials, and 4) the sensing wire. Principally, improvements of the junction, casing, and inner chamber backfill materials are being pursued. The junction material at the interface between the waste and the inner chamber of the reference electrode was identified as a critical component in the failure of the reference electrodes. Nine candidate replacement junction materials were tested under simulated waste conditions to evaluate permeation rate. These materials included a variety of polymeric and ceramic materials, some of which were 3-D printed. Thus far, porous polyvinylidene fluoride materials have performed satisfactorily and are being considered for prototype development. The commercial electrode casing materials in general have performed well. Additionally, 3-D printing of chemically and mechanically stable materials is being investigated as a means for further improvement in fabrication consistency. SRNL has also investigated altering the reference electrode design to extend the service life. The new design of the interior of the reference electrode casing creates a longer, more tortuous path between the junction material and the electrode sensing wire. A finite element model was used to optimize the design without adversely impacting the circuit resistance of the electrode during the measurements, thus preserving the measurement accuracy while enhancing the service life. The inner chamber back fill materials are also critical to the performance of the reference electrode. Materials that are resistant to intruding tank waste and provide a conductive path to the sensing wire were investigated. Gel and powder materials that are interspersed with a conductive chloride bearing material were tested for their influence on diffusion and electrode resistance. All the investigated materials and components will be assembled, with collaboration from commercial vendors, to fabricate the initial prototypes. Accelerated testing of the prototypes will be initiated in Year 2 of the program and will be completed in Year 3. A recommendation on the materials of construction and the design of the new robust reference electrode will be presented to the Hanford tank farm facility.

Sykes, Kiana [Savannah River National Laboratory (↗

Taylor approximation variance reduction for approximation errors in PDE-constrained Bayesian inverse problems

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors, i.e. the errors between the accurate parameter-to-observable mapping and the surrogate. The statistics of these errors are, however, in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline, i.e. before considering the data, the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to directly and efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.

Bayesian approximation error↗

Scattering neutrinos, spin models, and permutations

We consider a class of Heisenberg all-to-all coupled spin models inspired by neutrino interactions in a supernova with N degrees of freedom. These models are characterized by a coupling matrix that is relatively simple in the sense that there are only a few, relative to N , nontrivial eigenvalues, in distinction to the classic Heisenberg spin-glass models, leading to distinct behavior in both the high-temperature and low-temperature regimes. When the momenta of the neutrinos are uniform and random in directions, we can calculate the large- N partition function for the quantum Heisenberg model. In particular, the high-temperature partition function predicts a non-Gaussian density of states, providing interesting counterexamples showing the limits of general theorems on the density of states for quantum spin models. We can repeat the same argument for classical Heisenberg models, also known as rotor models, and we find the high-temperature expansion is completely controlled by the eigenvalues of the coupling matrix, and again predicts non-Gaussian behavior for the density of states as long as the number of eigenvalues does not scale linearly with N . Indeed, we derive the amusing fact that these partition functions are essentially the generating function for counting permutations in the high-temperature regime. Finally, for the case relevant to neutrinos in a supernova, we identify the low-temperature phase as a unique state with the direction of the momenta of the neutrino dictating its coherent state in flavor-space, a state we dub the “flavor-momentum-locked” state. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗