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Polyatomic molecular Dirac-Hartree-Fock calculations with Gaussian basis sets

Numerical methods have been used successfully in atomic Dirac-Hartree-Fock (DHF) calculations for many years. Some DHF calculations using numerical methods have been done on diatomic molecules, but while these serve a useful purpose for calibration, the computational effort in extending this approach to polyatomic molecules is prohibitive. An alternative more in line with traditional quantum chemistry is to use an analytical basis set expansion of the wave function. This approach fell into disrepute in the early 1980's due to problems with variational collapse and intruder states, but has recently been put on firm theoretical foundations. In particular, the problems of variational collapse are well understood, and prescriptions for avoiding the most serious failures have been developed. Consequently, it is now possible to develop reliable molecular programs using basis set methods. This paper describes such a program and reports results of test calculations to demonstrate the convergence and stability of the method.

Dyall, Kenneth G.

Physics-Based Machine Learning Methods for U-235 Forensics Signatures

Signatures of low-intensity U-235 sources have been recently studied by utilizing a variety of machine learning (ML) classifiers using features derived from gamma spectral measurements collected under structured campaigns. Several ML classifiers, such as ensemble of tress and classification trees, revealed misleadingly-optimistic training error due to over-fitting, and furthermore, their performance is not directly relatable to the physical properties due to their data-driven, opaque designs. We present a regression-based ML method that first estimates the inverse distance to the source and then utilizes a threshold to infer its presence, by representing the background as a source located at an infinite distance. For the inverse distance estimation, we study the ensemble of trees and Gaussian process regression methods, and a hyper parameter auto-tuning and selection method that employs five regression estimators. These methods avoid the over-fitting observed in several ML classifiers, while providing the classification error nearly comparable to them based on independent test data. Their error is directly related to estimates of the inverse physical distance to source, and the precision of error determines the seperability property that determines the false alarm and missed detection rates. The property of monotonic decrease of the source strength with increasing detector distance combined with Poisson distribution of measurements is utilized to analytically validate these methods by deriving the generalization equations of underlying regression methods.

Rao, Nageswara

Experimental results of active control on a large structure to suppress vibration

Three design methods, Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR), H-infinity, and mu-synthesis, are used to obtain compensators for suppressing the vibrations of a 10-bay vertical truss structure, a component typical of what may be used to build a large space structure. For the design process the plant dynamic characteristics of the structure were determined experimentally using an identification method. The resulting compensators were implemented on a digital computer and tested for their ability to suppress the first bending mode response of the 10-bay vertical truss. Time histories of the measured motion are presented, and modal damping obtained during the experiments are compared with analytical predictions. The advantages and disadvantages of using the various design methods are discussed.

Dunn, H. J.

Polarization-agnostic continuous-variable quantum key distribution

Here, we introduce a polarization-agnostic method for Gaussian-modulated coherent-state (GCMS) continuous-variable quantum key distribution (CVQKD). Due to the random and continuous nature of the GCMS protocol, Alice, the transmitter, can encode two distinct quadratures in each of two orthogonal polarization modes, such that Bob, the receiver, measures valid GCMS quadratures in a single polarization mode even when polarization changes occur during transmission. This method does not require polarization correction in the optical domain, does not require monitoring both polarization modes, reduces loss by eliminating optical components, and avoids the noise injected by polarization correction algorithms.

Williams, Brian P. [Oak Ridge National Laboratory

Parameter estimation for slit-type scanning sensors

The Infrared Astronomical Satellite, scheduled for launch into a 900 km near-polar orbit in August 1982, will perform an infrared point source survey by scanning the sky with slit-type sensors. The description of position information is shown to require the use of a non-Gaussian random variable. Methods are described for deciding whether separate detections stem from a single common source, and a formulism is developed for the scan-to-scan problems of identifying multiple sightings of inertially fixed point sources for combining their individual measurements into a refined estimate. Several cases are given where the general theory yields results which are quite different from the corresponding Gaussian applications, showing that argument by Gaussian analogy would lead to error.

Fowler, J. W.

Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations

A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.

Soh, Woo Y.

The CACAO Method for Smoothing, Gap Filling, and Characterizing Seasonal Anomalies in Satellite Time Series

Consistent, continuous, and long time series of global biophysical variables derived from satellite data are required for global change research. A novel climatology fitting approach called CACAO (Consistent Adjustment of the Climatology to Actual Observations) is proposed to reduce noise and fill gaps in time series by scaling and shifting the seasonal climatological patterns to the actual observations. The shift and scale CACAO parameters adjusted for each season allow quantifying shifts in the timing of seasonal phenology and inter-annual variations in magnitude as compared to the average climatology. CACAO was assessed first over simulated daily Leaf Area Index (LAI) time series with varying fractions of missing data and noise. Then, performances were analyzed over actual satellite LAI products derived from AVHRR Long-Term Data Record for the 1981-2000 period over the BELMANIP2 globally representative sample of sites. Comparison with two widely used temporal filtering methods-the asymmetric Gaussian (AG) model and the Savitzky-Golay (SG) filter as implemented in TIMESAT-revealed that CACAO achieved better performances for smoothing AVHRR time series characterized by high level of noise and frequent missing observations. The resulting smoothed time series captures well the vegetation dynamics and shows no gaps as compared to the 50-60% of still missing data after AG or SG reconstructions. Results of simulation experiments as well as confrontation with actual AVHRR time series indicate that the proposed CACAO method is more robust to noise and missing data than AG and SG methods for phenology extraction.

LAI

Comparative Analysis of Type III Radio Bursts and Solar Flares: Spatial Localization and Correlation with Solar Flare Intensity

We present a comprehensive study of type III radio bursts and their association with solar flares of magnitude M1.0 and larger, as observed by four widely separated spacecraft (Parker Solar Probe, Solar Orbiter, STEREO-A, and Wind). Our main focus is the introduction and validation of two methods for localizing radio bursts using the available multispacecraft data. The first method utilizes intensity fitting with a circular Gaussian distribution, while the second method is based on the time arrival of radio bursts. We demonstrate the effectiveness of these methods through the analysis of a single type III burst event and compare their results with the traditional radio triangulation technique. Furthermore, we conduct a statistical study of 17 type III bursts associated with M- and X-class solar flares in years 2020–2022. Our findings suggest a possible correlation between solar flare intensities and longitudes, with east limb flares tending to be weaker than west limb flares. We also observe a systematic drift of radio burst longitudes toward the east, potentially explained by a poleward component of the local density gradient. Our results suggest a strong correlation between solar flare intensities and radio burst properties, enhancing our understanding of the relationship between solar flares and type III radio bursts.

Radio astronomy

Gaussian Decomposition of Laser Altimeter Waveforms

We develop a method to decompose a laser altimeter return waveform into its Gaussian components assuming that the position of each Gaussian within the waveform can be used to calculate the mean elevation of a specific reflecting surface within the laser footprint. We estimate the number of Gaussian components from the number of inflection points of a smoothed copy of the laser waveform, and obtain initial estimates of the Gaussian half-widths and positions from the positions of its consecutive inflection points. Initial amplitude estimates are obtained using a non-negative least-squares method. To reduce the likelihood of fitting the background noise within the waveform and to minimize the number of Gaussians needed in the approximation, we rank the "importance" of each Gaussian in the decomposition using its initial half-width and amplitude estimates. The initial parameter estimates of all Gaussians ranked "important" are optimized using the Levenburg-Marquardt method. If the sum of the Gaussians does not approximate the return waveform to a prescribed accuracy, then additional Gaussians are included in the optimization procedure. The Gaussian decomposition method is demonstrated on data collected by the airborne Laser Vegetation Imaging Sensor (LVIS) in October 1997 over the Sequoia National Forest, California.

Hofton, Michelle A.

An implicit time-marching method for studying unsteady flow with massive separation

A fully implicit time-marching method is developed such that all spatial derivatives are approximated using central differences, but no use is made of any artificial dissipation. The numerical method solves the discretized equations using Alternating Direction Implicit-Block Gaussian Elimination technique. The method is implemented in the unsteady analysis, which solves the incompressible Navier-Stokes equations in terms of vorticity and stream function in generalized orthogonal coordinates. A clustered conformal C-grid is employed, and every effort is made to resolve the various length scales in the flow problem. The metric discontinuity at the branch-cut is treated appropriately using analytic continuation. Introduction of the BGE reordering permits implicit treatment of the branch cut in the numerical method. The vorticity singularity at the cusped trailing edge is also appropriately treated. This accurate and efficient implicit method is used to study flow at Re = 1000, past a 12-percent thick symmetric Joukowski airfoil at high angle of attack 30 and 53 deg.

Osswald, G. A.

Maximum a posteriori Ly α estimator (MAPLE): band power and covariance estimation of the 3D Ly α forest power spectrum

We present a novel maximum a posteriori estimator to jointly estimate band powers and the covariance of the three-dimensional power spectrum (P3D) of Ly $\alpha$ forest flux fluctuations, called MAPLE. Our Wiener-filter based algorithm reconstructs a window-deconvolved P3D in the presence of complex survey geometries typical for Ly $\alpha$ surveys that are sparsely sampled transverse to and densely sampled along the line of sight. We demonstrate our method on idealized Gaussian random fields with two selection functions: (i) a sparse sampling of 30 background sources per square degree designed to emulate the current Dark Energy Spectroscopic Instrument; (ii) a dense sampling of 900 background sources per square degree emulating the upcoming Prime Focus Spectrograph Galaxy Evolution Survey. Our proof-of-principle shows promise, especially since the algorithm can be extended to marginalize jointly over nuisance parameters and contaminants, i.e. offsets introduced by continuum fitting. Our code is implemented in JAX and is publicly available on GitHub.

79 ASTRONOMY AND ASTROPHYSICS

Optimization of direct air capture processes using reactive transport models of adsorption-desorption cycles

In this study, we develop and implement a reactive transport model in COMSOL Multiphysics® to address the challenges of direct air carbon capture. The model is validated against experimental data and used to simulate the cyclic steady state of the adsorption-desorption process. The optimization of this model is achieved through advanced trust-region methods integrated with Gaussian Processes. Key decision variables, including adsorption and desorption times, desorption temperature and pressure, input velocity, bed porosity, column length, and radius were optimized to minimize the capture cost. After optimization, a sensitivity analysis revealed the complex interplay between the decision variables and their effect on the specific energy and cost of removing the CO 2 . We optimized the capture cost while taking into account the trade-off between energy consumption and productivity. The resulting minimum capture cost was determined to be 265.2 $/t-CO 2 , which aligns with expected values reported in the literature. Numerical results suggest the effectiveness of the optimization strategies applied, and underscore the importance of simultaneous decision variable selection in improving the performance in direct air capture processes. We also extend the modeling approach to a 2D axisymmetric model to better visualize CO₂ uptake and temperature profiles, revealing significant radial gradients during the regeneration step. As a main drawback, this enhanced model comes with a computational cost approximately 40 times higher than that of the 1D model.

Adsorption-desorption process

Quasi-optical beam tracing module development for millimeter-wave high-wavenumber collective scattering on the NSTX-U and EAST tokamaks

A Python3-based beam tracing code utilizing Quasi-Optics has been developed to track both incident and receiving beams in high-k collective millimeter wave scattering systems within magnetic fusion plasmas. In contrast to existing ray tracing codes that solely consider refraction, this beam tracing code incorporates diffraction phenomena, providing a more comprehensive calculation. Here, this enhanced capability allows for a more accurate calculation of the scattering volume and spatial resolution in high-k collective scattering systems, crucial for evaluating system performance and facilitating data analysis. Unlike Geometrical Optics, Quasi-Optics employs the complex eikonal method, representing a Gaussian beam as a collection of coupled rays to accurately preserve diffraction characteristics. The developed code is intended for application in NSTX-Upgrade and EAST high-k beam tracing analyses, targeting frequencies of 693 GHz and 270 GHz, respectively. The high-k system's primary objective is the observation of electron-scale instabilities. Employing a symplectic integrator, the code ensures numerical accuracy, assessed through the conservation of the Hamiltonian. With its precision and efficiency, the code facilitates rapid inter-shot analyses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Autonomous Nanoparticle Synthesis Guided by In Situ Multiscale Structural Characterization

Autonomous synthesis platforms promise rapid exploration of vast parameter spaces; yet, integrating in situ structural characterization in closed-loop synthesis optimization remains challenging. We demonstrate a realization of such a closed-loop platform coupled with a droplet-flow microreactor, in situ X-ray scattering methods (SAXS/WAXS), and Gaussian process optimization to synthesize citrate-reduced Au nanoparticles with targeted characteristics. The system efficiently explored ∼19,000 synthesis recipes through 365 experiments, achieving precise control over size (4–60 nm) and polydispersity (σ < 0.11) across large citrate/gold ratios, exceeding traditional synthesis boundaries (1–10). Beyond confirming classical Turkevich–Frens trends, partial-dependence analysis revealed strong nonlinear coupling among precursor, citrate, and pH effects. Combining quantitative SAXS/WAXS analysis with electron microscopy characterization, we uncovered that crystallite size (d c ) and particle size (d) follow d c = 0.18d + β, where synthesis chemistry controls the intercept β while maintaining a universal slope. This parallel-band structure enables independent tuning of crystallite domain size at fixed particle diameter through a combination of chloride, gold precursor, citrate, and pH contributions (cross-validated Spearman ρ = 0.7 ± 0.1). High-resolution electron microscopy shows multiple lattice-fringe orientations within single particles, directly confirming polycrystalline domains and the ability to tune d c at the fixed d. The platform’s validation includes indistinguishable static versus flowing measurements, stable droplet transport at 100 °C, and <5% run-to-run variation, establishing a robust framework for mapping and controlling multiscale nanoparticle structure across expansive chemical spaces. In conclusion, the developed closed-loop platform can be applied to a borad range of nanosyntheis processes.

77 NANOSCIENCE AND NANOTECHNOLOGY

Analysis of differential scanning calorimetry data for aged plutonium

Differential scanning calorimetry data for samples of a 52 year old plutonium alloy with 3.3 at. % Ga that were heated beyond the melting point is analyzed using transition state theory to find activation energies for the δ to ε and ε to liquid phase transitions. A Bayesian statistical method involving a Gaussian process model is used to find mean values and confidence intervals for the activation energies. The activation energy for the δ to ε phase transition increases by 3.3 ± 3.8% per decade, relative to the case when all age related plutonium lattice point defects have been removed through annealing. The corresponding increase in activation energy for the ε to liquid transition is shown to be 7.1 ± 1.8% per decade. It is postulated that the change in activation energy with age for both phase transitions is caused, in part, by the accumulation of the same type of lattice point defects associated with the observed increase in elastic bulk modulus over time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Artificial-intelligence-assisted analysis of 28 Si * → 7⁢𝛼 breakup data

Mid-weight 𝛼-conjugate nuclei are predicted to possess exotic toroid like resonances with high angular momenta. The search for these states in 28 Si* is the main point of two published experimental investigations of the peripheral 28 Si + 12 C reaction by Cao and collaborators and by Hannaman and collaborators. In this work, we develop a novel artificial intelligence (AI) based machine learning method utilizing the Gaussian Mixture Model (GMM) to analyze available experimental and theoretical data. Here, we additionally study the reaction with the Hybrid 𝛼-Cluster (H⁡𝛼⁢C) model. In all the examined data, our results suggest the presence of underlying structure which is close to that predicted for toroidal states.

Breakup reactions

Feasibility of Correlation-Aware Inference and Universal Precision Scaling in Bonse–Hart Ultra-Small-Angle Neutron Scattering

Bonse–Hart ultra-small-angle neutron scattering (USANS) provides access to micrometre-scale structure, but useful measurements often require long counting times. In this work, we test whether the expected smoothness of the scattering profile can be exploited to improve data quality at lower counting statistics. We apply a Gaussian-process-based method to Bonse–Hart USANS data and evaluate its performance on pseudo-measurements generated from high-statistics experiments under Poisson statistics. This provides a stringent test of how well the underlying I(Q) profile can be reconstructed when the available counts are substantially reduced. We further show that, in the counting-limited regime, the reconstruction error follows a universal scaling behaviour that differs from the usual independent-counting expectation. At higher counts, the improvement crosses over to a resolution-limited regime set by analyser-angle discretization and rocking-curve width. These results clarify when correlation-aware inference is useful in USANS and provide a practical basis for improving measurement efficiency and beam-time usage.

Tung, Chi-Huan [ORNL] (ORCID:0000000221972074)

Generalized Airy functions for use in one-dimensional quantum mechanical problems

The solution of the one dimensional, time independent, Schroedinger equation in which the energy minus the potential varies as the nth power of the distance is obtained from proper linear combinations of Bessel functions. The linear combinations called generalized Airy functions, reduce to the usual Airy functions Ai(x) and Bi(x) when n equals 1 and have the same type of simple asymptotic behavior. Expressions for the generalized Airy functions which can be evaluated by the method of generalized Gaussian quadrature are obtained.

Eaves, J. O.