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All sources NASA NTRS DOE OSTI

DOE OSTI2023

Trajectory sampling and finite-size effects in first-principles stopping power calculations

Abstract Real-time time-dependent density functional theory (TDDFT) is presently the most accurate available method for computing electronic stopping powers from first principles. However, obtaining application-relevant results often involves either costly averages over multiple calculations or ad hoc selection of a representative ion trajectory. We consider a broadly applicable, quantitative metric for evaluating and optimizing trajectories in this context. This methodology enables rigorous analysis of the failure modes of various common trajectory choices in crystalline materials. Although randomly selecting trajectories is common practice in stopping power calculations in solids, we show that nearly 30% of random trajectories in an FCC aluminum crystal will not representatively sample the material over the time and length scales feasibly simulated with TDDFT, and unrepresentative choices incur errors of up to 60%. We also show that finite-size effects depend on ion trajectory via “ouroboros” effects beyond the prevailing plasmon-based interpretation, and we propose a cost-reducing scheme to obtain converged results even when expensive core-electron contributions preclude large supercells. This work helps to mitigate poorly controlled approximations in first-principles stopping power calculations, allowing 1–2 order of magnitude cost reductions for obtaining representatively averaged and converged results.

36 MATERIALS SCIENCE↗

DOE OSTI2020

An extended trajectory-mechanics approach for calculating two-phase flow paths

A technique originating in quantum dynamics is used to derive a trajectory-based, semi-analytical solution for two-phase flow. The partial differential equation governing the evolution of the aqueous phase is equivalent to a family of ordinary differential equations defined along a path through the porous medium. The trajectories may be found by solving the differential equations directly or by post-processing the output of a numerical solution to the full set of governing equations. The trajectories, which differ from conventional streamlines, are found to bend downward in response to gravitational forces. The curvature is more pronounced as the dip of the porous layer containing the flow increases. Subtle changes in the relative permeability curve can lead to significant variations in the trajectories. The ordinary differential equation for the trajectory provides an expression for the travel time along the path. The expression produces a semi-analytical approximation to the model parameter sensitivities, the partial derivatives of the travel times with respect to changes in the permeability model. The semi-analytical trajectory-based sensitivities generally agree with those computed using a numerical reservoir simulator and a perturbation approach. The sensitivities are useful in tomographic imaging algorithms designed to estimate the spatial variation in permeability within a porous medium using multiphase observations.

58 GEOSCIENCES↗

DOE OSTI2026

ARM Trajectories Data Set Value-Added Product Report

The U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility’s ARM Trajectories Data Set (ARMTRAJ) Value-Added Product (VAP) provides trajectory data sets initialized at ARM deployment coordinates and configured using ARM data sets. The four trajectory data sets support aerosol, cloud, and planetary boundary-layer research. Trajectory calculations use the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model informed by the European Centre for Medium-Range Weather Forecasts (ECMWF) fifth-generation atmospheric reanalysis (ERA5) data set at its highest spatial resolution (~31 km). HYSPLIT also runs at multiple initial starting locations surrounding ARM deployments (in latitude/longitude and/or vertical coordinates), facilitating an ensemble for each sample in the data sets. The ensemble mean and variability reported in ARMTRAJ improve the fidelity and provide uncertainty estimates of trajectory coordinates, thermodynamic properties, and other output fields.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

ARM Trajectories Data Set Value-Added Product Report

The U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility’s ARM Trajectories Data Set (ARMTRAJ) Value-Added Product (VAP) provides trajectory data sets initialized at ARM deployment coordinates and configured using ARM data sets. The six trajectory data sets support aerosol, cloud, planetary boundary layer, and related research (aerosol-cloud interactions, etc.), as well as studies using ARM Aerial Facility (AAF) and tethered balloon system (TBS) measurements. Trajectory calculations use the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model informed by the European Centre for Medium-Range Weather Forecasts (ECMWF) fifth-generation atmospheric reanalysis (ERA5) data set at its highest spatial resolution (~31 km). HYSPLIT also runs at multiple initial starting locations surrounding ARM deployments (in latitude/longitude and/or vertical coordinates), facilitating an ensemble for each sample in the data sets. The ensemble mean and variability reported in ARMTRAJ improve the fidelity and provide uncertainty estimates of trajectory coordinates, thermodynamic properties, and other output fields.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Vehicle trajectory prediction near or at traffic signal

A system and method for determining a predicted trajectory of a human-driven host vehicle as the human-driven host vehicle approaches a traffic signal. The method includes: obtaining a host vehicle-traffic light distance d x and a longitudinal host vehicle speed v x that are each taken when the human-driven host vehicle approaches the traffic signal; obtaining a traffic light signal phase P t and an traffic light signal timing T t ; obtaining a time of day TOD; providing the host vehicle-traffic light distance d x , the longitudinal host vehicle speed v x , the traffic light signal phase P t , the traffic light signal timing T t , and the time of day TOD as input into an artificial intelligence (AI) vehicle trajectory prediction application, wherein the AI vehicle trajectory prediction application implements an AI vehicle trajectory prediction model; and determining the predicted trajectory of the human-driven host vehicle using the AI vehicle trajectory prediction application.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Extracting Vehicle Trajectories from Partially Overlapping Roadside Radar

This work presents a methodology for extracting vehicle trajectories from six partially-overlapping roadside radars through a signalized corridor. The methodology incorporates radar calibration, transformation to the Frenet space, Kalman filtering, short-term prediction, lane-classification, trajectory association, and a covariance intersection-based approach to track fusion. The resulting dataset contains 79,000 fused radar trajectories over a 26-h period, capturing diverse driving scenarios including signalized intersections, merging behavior, and a wide range of speeds. Compared to popular trajectory datasets such as NGSIM and highD, this dataset offers extended temporal coverage, a large number of vehicles, and varied driving conditions. The filtered leader–follower pairs from the dataset provide a substantial number of trajectories suitable for car-following model calibration. The framework and dataset presented in this work has the potential to be leveraged broadly in the study of advanced traffic management systems, autonomous vehicle decision-making, and traffic research.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2026

Automated Classification of Vehicle Movements at Signalized Intersections Using Vehicle Trajectories

Accurate vehicle movement classification through signalized intersections is of paramount importance to the analysis of intersection performance and the optimization of traffic control strategies. Conventional techniques for tracking vehicle turning movements depend on infrastructure-based strategies like human counts, loop detectors, and video analytics, all of which are costly, prone to errors, and spatially constrained. High-frequency trajectory data can be utilized to determine vehicle movement patterns in a scalable and infrastructure-independent method due to the adoption of connected vehicles (CVs). In recent years, several studies have utilized connected vehicle data to generate performance measures. Most of the trajectory-based performance measures approaches, however, require map matching-i.e., extracting geospatial references from maps to identify the movements that individual vehicles make at a signalized intersection. These approaches are often time-consuming and hinder scalability since geographic features need to be provided for an analysis to be conducted. Map matching methods are prone to errors as different map versions change these geographic features. This research presents a novel automatic classification pipeline that uses CV trajectory data to classify vehicle movements at signalized crossings, specifically pass-through left-turn and right-turn maneuvers. The process starts by filtering trips that cross a spatial bounding box that has been defined at the target intersection. Approach and departure headings for each trajectory crossing the boundary are computed and are clustered together to identify dominant movements. The proposed algorithm is used to classify the movement of vehicles at 10 intersections in the state of California, and the results indicate that the algorithm can classify movements at these intersections with varying traffic volumes and road network configurations, all in a map-less framework with no need for conflation of vehicle trajectories to a digital base map.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Significance of Energy Conservation in Coupled-Trajectory Approaches to Nonadiabatic Dynamics

Practical methods for simulating photo-induced dynamics of molecules often rely on a trajectory-description of the nuclear dynamics, incorporating approximate electron-nuclear feedback. Through approximating electron–nuclear correlation terms in the exact factorization approach, trajectory-based methods have been derived and successfully applied to the dynamics of a variety of light-induced molecular processes, capturing quantum (de)coherence effects rigorously. These terms account for the coupling among the trajectories, recovering the nonlocal nature of quantum nuclear dynamics that is completely overlooked in traditional independent-trajectory algorithms. Nevertheless, some of the approximations introduced in the derivation of some of these methods do not conserve the total energy. We analyze energy conservation in the coupled trajectory mixed quantum-classical (CTMQC) algorithm and explore the performance of a modified algorithm, CTMQC-E, where some of the terms are redefined to restore energy conservation. Here, a set of molecular models is used as a test, namely, 2-cis-penta-2,4-dienimium cation, bis(methylene) adamantyl radical cation, butatriene cation, uracil radical cation, and neutral pyrazine.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Analytic solutions for Asay foil trajectories with implications for ejecta source models and mass measurements

We consider the trajectory of an Asay foil ejecta diagnostic for scenarios where ejecta are produced at a singly shocked planar surface and fly ballistically through a perfect vacuum to the sensor. We do so by building upon a previously established mathematical framework derived for the analytic study of stationary sensors. First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source model. The result is an integrodifferential equation of motion for the foil trajectory. This equation yields an easily calculable closed-form implicit solution for the foil trajectory in instant-production scenarios. From there, we derive a boundary condition that particle velocity distributions must satisfy if their associated foil trajectories are to exhibit a smooth initial acceleration, as occurs in some experiments. This condition is identical to one derived previously from a consideration of piezoelectric voltage data obtained in similar experiments. We also compare techniques for inferring accumulated ejecta masses from foil trajectories, first by deriving the exact solution, and then by quantifying the error imposed by a frequently used approximate solution (both subject to the assumption of instantaneous ejecta production). Finally, we examine the common practice of presenting inferred cumulative ejecta masses as a function of implied ejecta velocity, establishing the conditions under which this methodology is most meaningful.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Nonadiabatic dynamics with classical trajectories: The problem of an initial coherent superposition of electronic states

Advances in coherent light sources and development of pump–probe techniques in recent decades have opened the way to study electronic motion in its natural time scale. When an ultrashort laser pulse interacts with a molecular target, a coherent superposition of electronic states is created and the triggered electron dynamics is coupled to the nuclear motion. A natural and computationally efficient choice to simulate this correlated dynamics is a trajectory-based method where the quantum-mechanical electronic evolution is coupled to a classical-like nuclear dynamics. These methods must approximate the initial correlated electron–nuclear state by associating an initial electronic wavefunction to each classical trajectory in the ensemble. Different possibilities exist that reproduce the initial populations of the exact molecular wavefunction when represented in a basis. We show that different choices yield different dynamics and explore the effect of this choice in Ehrenfest, surface hopping, and exact-factorization-based coupled-trajectory schemes in a one-dimensional two-electronic-state model system that can be solved numerically exactly. Furthermore, this work aims to clarify the problems that standard trajectory-based techniques might have when a coherent superposition of electronic states is created to initialize the dynamics, to discuss what properties and observables are affected by different choices of electronic initial conditions and to point out the importance of quantum-momentum-induced electronic transitions in coupled-trajectory schemes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Multi‐Sensor Trajectory Reconstruction of the 24 April 2025 Alaska Fireball and Implications for Planetary Defense

On 24 April 2025 at 18:30:57 UTC, a bright daytime fireball over Southcentral Alaska was detected by 37 seismic stations, 16 single infrasound sensors, and four infrasound arrays, yielding 30 ballistic and multiple fragmentation arrivals. Here, the unprecedented density of seismoacoustic coverage enabled detailed reconstruction of the event using acoustic signals, with fragmentation source locations further guiding the identification of Doppler weather radar signatures of a meteorite fall. Incorporation of a radar-derived terminal point yielded a final trajectory solution, which agreed closely with an independent optical trajectory solution from video analysis. The reconstructed entry parameters from seismoacoustic analysis indicate a velocity of 25.3 km/s, an entry angle of 19°, and an energy release of ∼38 t TNT equivalent. Assuming a chondritic composition, the pre-entry object diameter was ∼0.7 m. Using orbital parameters from the optical solution, we estimate meteoroid composition as most likely an L-type ordinary chondrite. The event occurred in the sub-Arctic, where space-based optical systems face challenges in detection, demonstrating the critical role of dense ground-based seismoacoustic networks in characterizing high-latitude atmospheric entries. This uniquely well-recorded event demonstrates the capability of dense seismoacoustic networks to constrain bolide trajectories, energetics, and fragmentation, with radar and optical data providing critical confirmation and complementary perspectives. These results bridge the methodological gap between planetary-defense monitoring of natural impactors and space-traffic analyses of artificial reentries, illustrating how multi-sensor integration can deliver calibration-grade trajectories even for unpredicted events.

Fireball↗

DOE OSTI2023

Neutral gas pressure dependence of ion–ion mutual neutralization rate constants using Landau–Zener theory coupled with trajectory simulations

In this computational study, we describe a self-consistent trajectory simulation approach to capture the effect of neutral gas pressure on ion–ion mutual neutralization (MN) reactions. The electron transfer probability estimated using Landau–Zener (LZ) transition state theory is incorporated into classical trajectory simulations to elicit predictions of MN cross sections in vacuum and rate constants at finite neutral gas pressures. Electronic structure calculations with multireference configuration interaction and large correlation consistent basis sets are used to derive inputs to the LZ theory. The key advance of our trajectory simulation approach is the inclusion of the effect of ion-neutral interactions on MN using a Langevin representation of the effect of background gas on ion transport. For H + – H – and Li + – H(D) – , our approach quantitatively agrees with measured speed-dependent cross sections for up to ~10 5 m/s. For the ion pair Ne + – Cl – , our predictions of the MN rate constant at ~1 Torr are a factor of ~2 to 3 higher than the experimentally measured value. Similarly, for Xe + – F – in the pressure range of ~20 000–80 000 Pa, our predictions of the MN rate constant are ~20% lower but are in excellent qualitative agreement with experimental data. Here, the paradigm of using trajectory simulations to self-consistently capture the effect of gas pressure on MN reactions advanced here provides avenues for the inclusion of additional nonclassical effects in future work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Revealing Excited‐State Trajectories on Potential Energy Surfaces with Atomic Resolution in Real Time

Abstract Photoexcited molecular trajectories on potential energy surfaces (PESs) prior to thermalization are intimately connected to the photochemical reaction outcome. The excited‐state trajectories of a diplatinum complex featuring photo‐activated metal–metal σ ‐bond formation and associated Pt−Pt stretching motions were detected in real time using femtosecond wide‐angle X‐ray solution scattering. The observed motions correspond well with coherent vibrational wavepacket motions detected by femtosecond optical transient absorption. Two key coordinates for intersystem crossing have been identified, the Pt−Pt bond length and the orientation of the ligands coordinated with the platinum centers, along which the excited‐state trajectories can be projected onto the calculated PESs of the excited states. This investigation has gleaned novel insight into electronic transitions occurring on the time scales of vibrational motions measured in real time, revealing ultrafast nonadiabatic or non‐equilibrium processes along excited‐state trajectories involving multiple excited‐state PESs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Revealing Excited‐State Trajectories on Potential Energy Surfaces with Atomic Resolution in Real Time

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Silica nanocluster binding rate coefficients from molecular dynamics trajectory calculations

Oxide nanoparticle growth from vapor phase precursors occurs in high temperature aerosol reactors first via the formation of nanoclusters, which are nanometer-scale condensed-phase species composed of 10 1 -10 2 atoms. The binding rate for nanoclusters, defined as the rate at which two nanoclusters collide with and stick to one another, is hence of interest in predicting nanoparticle size distribution functions in an aerosol. We have utilized molecular dynamics (MD) trajectory calculations to determine the homogeneous (equal-sized) and heterogeneous (disparate-sized) binding rate coefficients of SiO2 (silica) nanoclusters composed of 18, 144, and 333 atoms. MD trajectory calculations incorporated all-atom models of nanoclusters using a combined Born–Huggins–Mayer-Lennard-Jones potential model, which accounts for both short range interactions and electrostatic interactions. MD calculations were utilized to determine the binding probability as a function of both initial relative velocity and impact parameter; integration of the binding probability across impact parameter and relative velocity space yields the binding rate coefficient. MD trajectory calculations reveal that the most common type of encounters between nanoclusters leading to binding are grazing collisions, i.e. instances where collision would not occur without induced dipole potential influences. The resulting binding rate coefficients are found to be extremely weakly dependent on system temperature, which is in contrast to the use of rate coefficient models which are the product of a hard-sphere collision rate coefficient and a constant enhancement factor (leading to a rate coefficient proportional to the square root of temperature). Enhancement factors defined from MD trajectory calculations fall in the range of 3–9 as system temperature decreases from 1500 K to 300 K. Furthermore, such large values suggest that potential interactions need to be considered when modeling oxide nanocluster growth in the gas phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

CryoTRANS: predicting high-resolution maps of rare conformations from self-supervised trajectories in cryo-EM

Cryogenic electron microscopy (cryo-EM) has revolutionized structural biology, enabling efficient determination of structures at near-atomic resolutions. However, a common challenge arises from the severe imbalance among various conformations of vitrified particles, leading to low-resolution reconstructions in rare conformations due to a lack of particle images in these quasi-stable states. We introduce CryoTRANS, a method that predicts high-resolution maps of rare conformations by constructing a self-supervised pseudo-trajectory between density maps of varying resolutions. This trajectory is represented by an ordinary differential equation parameterized by a deep neural network, ensuring retention of detailed structures from high-resolution density maps. By leveraging a single high-resolution density map, CryoTRANS significantly improves the reconstruction of rare conformations and has been validated on four real-world datasets: alpha-2-macroglobulin, actin-binding protein complexes, SARS-CoV-2 spike glycoprotein, and the 70S ribosome. CryoTRANS can also predict high-resolution structures in cryogenic electron tomography maps using a high-resolution cryo-EM map.Cryogenic electron microscopy (cryo-EM) has revolutionized structural biology, enabling efficient determination of structures at near-atomic resolutions. However, a common challenge arises from the severe imbalance among various conformations of vitrified particles, leading to low-resolution reconstructions in rare conformations due to a lack of particle images in these quasi-stable states. We introduce CryoTRANS, a method that predicts high-resolution maps of rare conformations by constructing a self-supervised pseudo-trajectory between density maps of varying resolutions. This trajectory is represented by an ordinary differential equation parameterized by a deep neural network, ensuring retention of detailed structures from high-resolution density maps. By leveraging a single high-resolution density map, CryoTRANS significantly improves the reconstruction of rare conformations and has been validated on four real-world datasets: alpha-2-macroglobulin, actin-binding protein complexes, SARS-CoV-2 spike glycoprotein, and the 70S ribosome. CryoTRANS can also predict high-resolution structures in cryogenic electron tomography maps using a high-resolution cryo-EM map.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Material coherence from trajectories via Burau eigenanalysis of braids

In this paper, we provide a numerical tool to study a material’s coherence from a set of 2D Lagrangian trajectories sampling a dynamical system, i.e., from the motion of passive tracers. We show that eigenvectors of the Burau representation of a topological braid derived from the trajectories have levelsets corresponding to components of the Nielsen–Thurston decomposition of the dynamical system. One can thus detect and identify clusters of space–time trajectories corresponding to coherent regions of the dynamical system by solving an eigenvalue problem. Unlike previous methods, the scalable computational complexity of our braid-based approach allows the analysis of large amounts of trajectories.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Analytic and numerical vibronic spectra from quasi-classical trajectory ensembles

The truncated Wigner approximation to quantum dynamics in phase space is explored in the context of computing vibronic line shapes for monomer linear optical spectra. We consider multiple model potential forms including a shifted harmonic oscillator with both equal and unequal frequencies on the ground and excited state potentials as well as a shifted Morse potential model. For the equal-frequency shifted harmonic oscillator model, we derive an analytic expression for the exact vibronic line shape that emphasizes the importance of using a quantum mechanical distribution of phase space initial conditions. For the unequal-frequency shifted harmonic oscillator model, we are no longer able to obtain an exact expression for the vibronic line shape in terms of independent deterministic classical trajectories. We show how one can rigorously account for corrections to the truncated Wigner approximation through nonlinear responses of the line shape function to momentum fluctuations along a classical trajectory and demonstrate the qualitative improvement in the resulting spectrum when the leading-order quantum correction is included. Finally, we numerically simulate absorption spectra of a highly anharmonic shifted Morse potential model. We find that, while finite quantization and the dissociation limit are captured with reasonable accuracy, there is a qualitative breakdown of the quasi-classical trajectory ensemble’s ability to describe the vibronic line shape when the relative shift in Morse potentials becomes large. The work presented here provides clarity on the origin of unphysical negative features known to contaminate absorption spectra computed with quasi-classical trajectory ensembles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗