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Simultaneous imaging of vibrational, rotational, and electronic wave-packet dynamics in a triatomic molecule

Light-induced molecular dynamics often involve the excitation of several electronic, vibrational, and rotational states. Since the ensuing electronic and nuclear motion determines the pathways and outcomes of photoinduced reactions, our ability to monitor and understand these dynamics is crucial for molecular physics, physical chemistry, and photobiology. However, characterizing this complex motion represents a significant challenge when different degrees of freedom are strongly coupled. In this Letter, we demonstrate how the interplay between vibrational, rotational, and electronic degrees of freedom governs the evolution of molecular wave packets in the low-lying states of strong-field-ionized sulfur dioxide. Using time-resolved Coulomb explosion imaging (CEI) and quantum mechanical wave packet simulations, we directly map the bending vibrations of the molecule, show how the vibrational wave packet is influenced by molecular alignment, and elucidate the consequences of nuclear motion for the coupling between the two lowest electronic states of the cation. Furthermore, our results demonstrate that multicoincident CEI can be an efficient experimental tool for characterizing coupled electronic and nuclear motion in polyatomic molecules.

Atomic & molecular processes in external fields

RAIS Preliminary Remediation Goals for Radionuclides

Radionuclide PRGs (https://rais.ornl.gov/cgi-bin/prg/PRG_search?select=rad) are calculated by selecting the applicable radionuclide(s) together with the applicable media, land use, and exposure route combination. If “site-specific” is selected as the PRG type, the following page will show the equations and exposure parameters used for deriving the PRGs, and some of the parameter values may be changed as necessary. If “default” is selected as the PRG type, the RAIS will proceed directly to the results page. Multiple radionuclides can be selected with this tool. Results can be downloaded in .xlsx or .pdf formats. Additionally, the session inputs for the PRG calculator can be saved for future use and recalled by the PRG calculator. The derivation of the selected PRG(s) and the applicable equations and exposure parameters can be reviewed in more detail using the RAIS Radionuclide PRG Calculator User Guide available here: https://rais.ornl.gov/tools/rais_rad_prg_guide.html. html.

Manning, Karessa [Oak Ridge National Laboratory (O

User’s Manual for RESRAD-RDD&IND Code Version 2: Vol. 2—User’s Guide for RESRAD-RDD&IND Code

Version 2.0 of the RESRAD-RDD&IND computer code is designed to support the implementation of protective action guides (PAGs) after a nuclear emergency incident including a radiological dispersal device (RDD) and/or an improvised nuclear device (IND) incident (EPA 2017). Eight different group types, addressing various decisions, are available for selection. The RESRAD-RDD&IND code calculates radiological doses, stay times, etc., for the selected group that the user wishes to focus on. (That is, the results for all the groups are not calculated simultaneously, and the input for those other groups do not matter, although some parameter values are shared between groups.) Version 2.0 has a user-friendly interface so that the RESRAD-RDD&IND code can be used with minimal training. For example, the user can select the major characteristics of the problem-event type, source term, and decision type from the left side of the interface and then calculate the results with the default assumptions for the exposure scenarios. More in-depth analysis would include specifying site-specific exposure scenario characteristics in the right side of the interface. The procedures for data entry and results viewing are self-explanatory. This is because common window maneuvering features and text instructions were incorporated in the interface design. General and context-specific help are available to aid users entering parameter values, as well. The RESRAD-RDD&IND computer code gives the user the option to select either an RDD or IND incident for analysis. For an RDD event analysis, 11 radionuclides (Am-241, Cf-252, Cm-244, Co-60, Cs-137, Ir-192, Po-210, Pu-238, Pu-239, Ra-226, and Sr-90) are included. These 11 radionuclides are the radionuclides most likely used for an RDD. More than 90 radionuclides can be selected for an IND event analysis. Initial default concentrations are provided for 44 radionuclides for a uranium-fueled IND event. These 44 radionuclides are those that would contribute significantly to the radiation dose associated with a uranium-fueled bomb detonation. The radionuclides generated from ingrowth of these 44 initial radionuclides are also automatically included in the analysis. Pu-239, Cs-134m, Ru-105, and Rb-89 and their progeny can be selected for analysis if they are detected and their concentrations are determined. This user’s guide, which is Volume 2 of the User’s Manual for RESRAD-RDD&IND Code Version 2, provides instructions to users on how to install the RESRAD-RDD&IND code, navigate the interface, and use the various features, including those discussed above, to set up an analysis and view/print the results in text outputs. Volume 1 of the User’s Manual for RESRAD-RDD&IND Code Version 2 (Yu et al. 2026), which contains descriptions of the methodology and theoretical basis for dose modeling and the mathematical equations implemented in the code, can be accessed and viewed through the Help menu in the code or can be downloaded from the RESRAD website (https://resrad.evs.anl.gov).

22 GENERAL STUDIES OF NUCLEAR REACTORS

CLPNets: Coupled Lie–Poisson neural networks for multi-part Hamiltonian systems with symmetries

To accurately compute data-based prediction of Hamiltonian systems, it is essential to utilize methods that preserve the structure of the equations over time. We consider a particularly challenging case of systems with interacting parts that do not reduce to pure momentum evolution. Such systems are essential in scientific computations, such as discretization of a continuum elastic rod, which can be viewed as the group of rotations and translations $SE(3)$. The evolution involves not only the momenta but also the relative positions and orientations of the particles. The presence of Lie group-valued elements, such as relative positions and orientations, poses a problem for applying previously derived methods for data-based computing. We develop a novel method of data-based computation and complete phase space learning of such systems. We follow the original framework of SympNets (Jin et al., 2020) and LPNets (Eldred et al., 2024), building the neural network from phase space mappings that preserve the Lie–Poisson structure. We derive a novel system of mappings that are built into neural networks describing the evolution of such systems. We call such networks Coupled Lie–Poisson Neural Networks, or CLPNets. We consider increasingly complex examples for the applications of CLPNets, starting with the rotation of two rigid bodies about a common axis, progressing to the free rotation of two rigid bodies, and finally to the evolution of two connected and interacting $SE(3)$ components, describing the discretization of an elastic rod into two elements. Our method preserves all Casimir invariants to machine precision, preserves energy to high accuracy, and shows good resistance to the curse of dimensionality, requiring only a few thousand data points for all cases studied (three to eighteen dimensions). Additionally, the method is highly economical in memory requirements, requiring only about 200 parameters for the most complex case considered.

Data-based modeling

An–imidophosphorane (An = U–Pu) bond covalency and proton-coupled electron transfer thermodynamics driven by orbital energy matching

A series of mid-actinide (An = U–Pu) tetrahomoleptic complexes supported by highly electron-donating imidophosphorane ligands, NPC ([NP t Bu(pyrr) 2 ] − , where t Bu = C(CH 3 ) 3 ; pyrr = pyrrolidinyl = N(C 4 H 8 )), are systematically investigated computationally and experimentally to elucidate the nature of actinide–ligand (An–L) covalency across the An 3+/4+/5+ oxidation states. Trends in An–L bonding and redox properties for these complexes, together with their protonated counterparts, are examined using orbital-, electron density-, and energy-decomposition-based methods. This integrated approach reveals progressively improved energy matching between α-spin An 5f and N im 2p orbitals with increasing atomic number and oxidation state, becoming particularly pronounced in the ligand-dominant π-bonding orbitals of An 4+ and An 5+ . In contrast to the An 3+ species, the enhanced An 5f π contributions in the higher-valent counterparts drive the increase in An–N im covalency for later An, thereby inverting the covalency trend to U < Np < Pu. Redistribution of electron density towards the An and N im atomic basins due to the growing energy-matching assisted covalency correlates with higher pKa values and increased N im –H bond dissociation free energies in protonated An 4+ complexes. Electron density at Nim in An 4+ shows a linear correlation with the p K a values calculated via the Bordwell equation. Calculations predict a cathodic shift of 0.84–1.00 V in the redox couples upon protonation, a trend validated when experimentally accessible. These findings demonstrate an increasing role of covalency driven by orbital energy matching from U to Pu in tuning the thermodynamic driving force for proton-coupled electron transfer in the An 5+ species.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA

The Strength of Coupling to the Southern Ocean Modulates Tropical Eastern Pacific Variability and Forced Response

Despite rising global-mean temperatures, large parts of the Southern Ocean and tropical eastern Pacific Ocean have cooled during the satellite era. These regions may be linked by teleconnections, with Southern Ocean cooling contributing to tropical eastern Pacific cooling. We demonstrate that, on average, state-of-the-art Earth system models (ESMs) underestimate the magnitude of interaction between the Southern Ocean and tropical eastern Pacific Ocean. The strength of the teleconnection is shown to be mediated by the magnitude of the positive cloud–sea surface temperature (SST) feedback in the subtropical eastern Pacific Ocean and the strength of the wind–evaporation–SST (WES) feedback. We link excessive precipitation in the tropical Pacific south of the equator to the strength of the Southern Ocean–eastern Pacific teleconnection. This model bias, known as the double intertropical convergence zone (ITCZ), is shown to be related to erroneous convection south of the equator, weakened cross-equatorial trade winds, and unfavorable meteorological conditions for marine boundary layer subtropical clouds. We postulate there is a two-way interaction, in which a double-ITCZ occurs with weaker cloud–SST and WES feedbacks, which in turn impact local SSTs and amplify the double-ITCZ. Models with a stronger Southern Ocean to tropical Pacific teleconnection tend to exhibit more multidecadal variability in the Walker circulation, ITCZ, and west–east equatorial SST gradient, as well as greater delayed warming in the tropical eastern Pacific Ocean resulting from delayed Southern Ocean warming under greenhouse gas forcing. These results provide insight into why ESMs struggle to replicate observed tropical Pacific temperature trend patterns and point to ITCZ location as a key target for improvement in future model development.

Climate change

Identifying Differential Equations in Fourier Domain (FourierIdent)

We investigate identifying differential equations in the frequency domain. Fourier analysis is an important tool in theoretical analysis and numerical solvers of differential equations, yet there is limited work in exploring this connection in the identification of differential equations. This paper aims to identify the underlying differential equation in the frequency domain, from a given single realization of the differential equation perturbed by noise. Such setting imposes difficulties which are different from other identification methods where computation is carried out in the physical domain. We propose several ways to mitigate the challenges arising from noise in data and large differences in the magnitudes of frequency responses. The main takeaways are that identifying differential equations solely in the frequency domain is challenging, the method we propose is based on a form of domain partitions in the frequency domain, and this method shows benefits for complex data even with high level of noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain and to enhance the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms, and shows advantages on complex data with many frequency modes, even under high level of noise.

97 MATHEMATICS AND COMPUTING

Coupling to rotational manifolds to improve gas-phase pump–probe spectroscopic models

The physical picture of gas-phase optical transitions is normally presented as an isolated two-level system balanced by upward and downward processes. Isolated models assume a phenomenological treatment of collisional dephasing but do not strictly account for collisional population exchange with the rotational baths. While this assumption is valid under low-intensity conditions, where excitation is rate-limiting, isolated models can deviate from Beer’s Law at sufficient pressures and monochromatic intensities when both collisional broadening and power broadening are comparable to (or greater than) lifetime broadening, which are not uncommon conditions for cavity enhanced spectroscopies in the mid-IR spectral range. Although this problem has been addressed by rate-equation models for linear absorption measurements, a general treatment for multi-level quantum mechanical models suitable for non-linear absorption measurements (two-photon/two-color/pump–probe) is lacking. Isolated models require physical parameter inputs that disagree with expected values by at least an order of magnitude. These non-physical models undermine the ability to predict non-linear signal strengths under untested conditions and thereby limit the potential to optimize the sensitivity of non-linear spectroscopies and to expand their analytical applications (e.g., new analytes and/or buffer gases, changes in cavity free-spectral-range, changes in intracavity powers or wavelengths, and accurate investigation of physical phenomena). In this study, we derive bath-coupled models for gaseous pump–probe spectroscopy by application of the quantum Lindblad equation and detailed balance. Bath-coupled models are shown to fit data consistently across variations in intensity and agree with all physically expected values.

Cavity ring-down spectroscopy

Energy-momentum-conserving stochastic differential equations and algorithms for the nonlinear Landau-Fokker-Planck equation

Coulomb collision is a fundamental diffusion process in plasmas that can be described by the Landau-Fokker-Planck (LFP) equation or the stochastic differential equation (SDE). While energy and momentum are conserved exactly in the LFP equation, they are conserved only on average by the conventional corresponding SDEs, suggesting that the underlying stochastic process may not be well defined by such SDEs. Here, in this study, we derive new SDEs with exact energy-momentum conservation for the Coulomb collision by factorizing the collective effect of field particles into individual particles and enforcing Newton's third law. These SDEs, when interpreted in the Stratonovich sense, have a particularly simple form that represents pure diffusion between particles without drag. To demonstrate that the new SDEs correspond to the LFP equation, we develop numerical algorithms that converge to the SDEs and preserve discrete conservation laws. Simulation results are presented in a benchmark of various relaxation processes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Lossy Compression: An Online Multi-Stage Technology for High-Fidelity Synchro- Waveform Measurements

Effective real-time monitoring and analysis of distributed grids necessitate the use of synchro-waveform measurements, which capture almost all high-frequency disturbances and transient phenomena. However, due to limitations in high-speed measurements and network bandwidth, it is challenging to transfer all high-fidelity synchro-waveforms losslessly and successfully. To cope with these challenges, a hybrid-based online multi-stage compression algorithm is proposed to significantly improve the compression efficiency for synchro-waveform measurements. Initially, the multiple discrete Wavelet transformation is deployed to deconstruct the waveform components. The delta encoding is further developed to decrease the magnitude. In conjunction with the Lempel-Ziv-Markov chain, the hybrid compression algorithm is implemented to achieve real-time compression for the synchro-waveform measurements. Moreover, an innovative error index that synergizes the time and frequency domain error and correlation is formulated to evaluate the waveform distortion. By integrating compression ratio, suitable parameters can be optimally selected. Finally, the simulation, laboratory experiments, as well as field tests across a spectrum of sampling frequencies and time intervals are conducted to substantiate the efficacy of the proposed method. Here, the outcomes demonstrated that a compression ratio of approximately 15.5 and 17.83 can be reached for 0.5 s and 1 s data under both offline and online scenarios, which equates to a substantial 93.5% to 94.39% reduction in data storage requirements.

High-fidelity synchro-waveform measurements

Resolving turbulent magnetohydrodynamics: a hybrid operator-diffusion framework

We present a hybrid machine learning framework that combines physics-informed neural operators (PINOs) with score-based generative diffusion models to simulate the full spatio-temporal evolution of two-dimensional, incompressible, resistive magnetohydrodynamic turbulence across a broad range of Reynolds numbers (Re). The framework leverages the equation-constrained generalization capabilities of PINOs to predict coherent, low-frequency dynamics, while a conditional diffusion model stochastically corrects high-frequency residuals, enabling accurate modeling of fully developed turbulence. Trained on a comprehensive ensemble of high-fidelity simulations with Re ϵ {100, 250, 500, 750, 1000, 3000, 10000}, the approach achieves state-of-the-art accuracy in regimes previously inaccessible to deterministic surrogates. At Re = 1000 and 3000, the model faithfully reconstructs the full spectral energy distributions of both velocity and magnetic fields late into the simulation, capturing non-Gaussian statistics, intermittent structures, and cross-field correlations with high fidelity. At extreme turbulence levels (Re = 10 000), it remains the first surrogate capable of recovering the high-wavenumber evolution of the magnetic field, preserving large-scale morphology and enabling statistically meaningful predictions.

Diffusion-Integrated Neural Operators

Stability-preserving Lossy Compression for Large-scale Partial Differential Equations

Checkpoint/Restart (C/R) strategies are vital for fault tolerance in PDE-based scientific simulations, yet traditional checkpointing incurs significant I/O overhead. Lossy compression offers a scalable solution by reducing checkpoint data size, but conventional methods often lack control over physical invariants (e.g., energy), leading to instability such as oscillations or divergence in Partial Differential Equations (PDE) systems. This paper introduces a stability-preserving compression approach tailored for PDE simulations by explicitly controlling kinetic and potential energy perturbations to ensure stable restarts. Extensive experiments conducted across diverse PDE configurations demonstrate that our method maintains numerical stability with minimal error magnification—even across multiple checkpoint-restart cycles—outperforming state-of-the-art lossy compressors. Parallel evaluations on the Frontier supercomputer show up to 8.4× improvement in checkpoint write performance and 6.3× in read performance, while maintaining relative L2 errors ∼ 2e-6 throughout continued simulation. These results provide practical guidance for balancing compression accuracy, stability, and computational efficiency in large-scale PDE applications.

Gong, Qian [ORNL] (ORCID:0000000235704142)

Polynomial range estimation as a troubled-cell indicator for high-order methods

Two troubled-cell indicators based on polynomial range estimation methods are used to flag cells that may violate positivity constraints. One method uses interval extension, and the second uses the range enclosure property of the Bernstein polynomial basis. Furthermore, both methods reduce compute time for the positivity preserver by limiting its application to a subset of cells. The Bernstein polynomial method remains effective as the problem dimensionality increases. Interval extension applied to the internal energy equation permits the use of the troubled-cell indicators for rational functions, though performance suffers compared to directly applying the indicators to polynomial functions.

42 ENGINEERING

Scalar flux transport models for self-similar turbulent mixing

A common approach to closing turbulent species flux in multicomponent Reynolds-averaged Navier-Stokes models is to use the standard gradient diffusion approximation. While such an approach has been shown to work well when applied to many canonical turbulent mixing configurations, a gradient diffusion approach is fundamentally limited in its ability to capture complex phenomena such as countergradient transport. For this reason, complicated mixing applications may benefit by treating the turbulent diffusivity with a model transport equation in a manner analogous to second-moment momentum closure in Reynolds-stress transport models. Here, the present work explores the development and application of two different scalar flux transport (SFT) models. Self-similarity constraints are derived for these models, and they are evaluated against gradient-diffusion-based models in several one- and two-dimensional problems of turbulent mixing. It is found that the new SFT models out-perform gradient diffusion models in problems involving rapid acceleration reversal and in problems involving anisotropic transport of materials. In addition, it is found that even a hybrid-SFT approach, in which an SFT equation is utilized along with a gradient diffusion closure, provides some measure of improvement over models that transport the mass flux rather than the scalar flux.

Reynolds-averaged Navier Stokes

Simple Heat Transfer Model for Film Cooling Applications

This report describes the development of a simple engineering model for film cooling. This model is used to derive a relationship between local wall temperature variations and key cooling performance parameters like local heat transfer coefficients and film effectiveness. This relation and method new and different from previously published models. The scope of this report includes the derivation of regression model equations for a flat plate with and without film cooling. The model equation for a flat plate without film cooling can be used to estimate local heat transfer coefficients using surface temperatures measured from infrared thermography. The model equation for the flat plate with film cooling can be used to estimate film cooling effectiveness, $η_f$, and heat transfer augmentation from the film cooling jet(s).

42 ENGINEERING

Stacked networks improve physics-informed training: Applications to neural networks and deep operator networks

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can happen to be difficult or impossible to train accurately. Here, we present a novel multifidelity framework for stacking physics-informed neural networks and operator networks that facilitates training. We successively build a chain of networks, where the output at one step can act as a low-fidelity input for training a longer chain, gradually increasing the expressivity of the learnt model. The equations imposed at each step of the iterative process can be the same or different (akin to simulated annealing). The iterative (stacking) nature of the proposed method allows us to learn progressively features of a solution which could have been hard to learn directly. Through benchmark problems including a nonlinear pendulum, the wave equation, and the viscous Burgers equation, we show how stacking can be used to improve the accuracy and reduce the required size of physics-informed neural networks and operator networks.

97 MATHEMATICS AND COMPUTING

Mapping Incidence and Prevalence Peak Data for SIR Modeling Applications

Infectious disease modeling and forecasting have played a key role in helping assess and respond to epidemics and pandemics. Recent work has leveraged data on disease peak infection and peak hospital incidence to fit compartmental models for the purpose of forecasting and describing the dynamics of a disease outbreak. Incorporating these data can greatly stabilize a compartmental model fit on early observations, where slight perturbations in the data may lead to model fits that forecast wildly unrealistic peak infection. We introduce a new method for incorporating historic data on the value and time of peak incidence of hospitalization into the fit for a Susceptible-Infectious-Recovered (SIR) model by formulating the relationship between an SIR model’s starting parameters and peak incidence as a system of two equations that can be solved computationally. We demonstrate how to calculate SIR parameter estimates – which describe disease dynamics such as transmission and recovery rates – using this method, and determine that there is a noticeable loss in accuracy whenever prevalence data is misspecified as incidence data. To exhibit the modeling potential, we update the Dirichlet-Beta State Space modeling framework to use hospital incidence data, as this framework was previously formulated to incorporate only data on total infections. This approach is assessed for practicality in terms of accuracy and speed of computation via simulation.

97 MATHEMATICS AND COMPUTING

Results of an interlaboratory study on the working curve in vat photopolymerization II: Towards a standardized method

The working curve measurement in photopolymer additive manufacturing is a ubiquitous measure of the cure depth of a printing resin as a function of radiant exposure of light. The fit parameters from this measurement (the depth of light penetration D p and the critical exposure E c ) are used to evaluate and report a resin’s printability, optimize processing parameters, and inform print and resin quality control. Despite its widespread use, the working curve lacks a standard measurement method. Here, following up on our paper “Results of an Interlaboratory Study on the Working Curve in Vat Photopolymerization” from last year, an interlaboratory study on the working curve was performed using calibrated, reproducible, bandpass filtered light sources. With these light sources, the variability between labs in measured working curves was dramatically reduced from the initial interlaboratory study. Aggregate data from this experiment produced reliable D p and E c measurements at 385 nm of 39.2 ± 3.7 µm and 12.3 ± 3.0 mJ cm −2 , respectively. At 405 nm the values of D p and E c are 69.3 ± 3.8 µm and 17.9 ± 2.3 mJ cm −2 , respectively. The results are agnostic to the thickness measurement tool utilized by participants, ensuring broad applicability across laboratories. We also tested the generalizability of the proposed method of using a filtered light source by filtering a commercial 405 nm light source and obtaining a working curve in agreement with the aggregate data from the interlaboratory study. This interlaboratory study provides a basis for a documentary standard for the working curve, so that the entire photopolymer additive manufacturing industry can share reproducible and interoperable working curve data.

36 MATERIALS SCIENCE