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DOE OSTI2025

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↗

DOE OSTI2024

Shearless effective barriers to chaotic transport induced by even twin islands in nontwist systems

For several decades now it has been known that systems with shearless invariant tori, nontwist Hamiltonian systems, possess barriers to chaotic transport. These barriers are resilient to breakage under perturbation and therefore regions where they occur are natural places to look for barriers to transport. Here we describe a kind of effective barrier that persists after the shearless torus is broken. Because phenomena are generic, for convenience we study the standard nontwist map (SNM), an area-preserving map that violates the twist condition locally in the phase space. The barrier occurs in nontwist systems when twin even period islands are present, which happens for a broad range of parameter values in the SNM. With a phase space composed of regular and irregular orbits, the movement of chaotic trajectories is hampered by the existence of shearless curves, total barriers, and a network of partial barriers formed by the stable and unstable manifolds of the hyperbolic points. Being a degenerate system, the SNM has twin islands and, consequently, twin hyperbolic points. We show that the structures formed by the manifolds intrinsically depend on period parity of the twin islands. For this even scenario the structure that we call a torus free barrier occurs because the manifolds of different hyperbolic points form an intricate chain atop a dipole configuration and the transport of chaotic trajectories through the chain becomes a rare event. This structure impacts the emergence of transport, the escape basin for chaotic trajectories, the transport mechanism, and the chaotic saddle. The case of odd periodic orbits is different: we find for this case the emergence of transport immediately after the breakup of the last invariant curve, and this leads to a scenario of higher transport, with intricate escape basin boundary and a chaotic saddle with nonuniformly distributed points.

classical mechanics↗

DOE OSTI2026

Uncertainty-Driven Rapid Thermodynamic Assessment of Nb-Ta-Zr System and Effects of C impurities (L25GF9298S): Annual Progress Report

An integrated computational materials engineering (ICME) method is in development for rapid thermodynamic experimental investigation and high-fidelity computational modeling of refractory multi-principal element alloys (RMPEAs). These ultra-high-temperature (UHT) alloys are of interest for structural applications in extreme environments, but deficiency of reliable data, especially melting temperatures, impedes the prediction of alloys with favorable properties. The method leverages UHT capabilities and computational expertise of LLNL’s Materials Science Division and the McCormack Lab’s UHT conical nozzle levitation (CNL) system to iteratively map the Nb-Ta-Zr phase space, with focus on the liquidus surface, through targeted experiments selected by quantifying uncertainty in the thermodynamic model fitting parameters. This method will reduce the time to map uncharted RMPEA phase space and thereby accelerate discovery and development of advanced materials for applications in extreme environments.

36 MATERIALS SCIENCE↗

DOE OSTI2025

First Order Transport of a Cold Uniform Ellipsoid of Charge

A single particle has a 6-element phase space vector $s = (x, γv)$ where $γv =\frac{p}{m}$ s proportional to the relativistic momentum. The ellipsoid is represented by a 21-element vector $(s, C, V)$ where $s$ is the phase space location of the centroid. $C$ is the 3 × 3 covariance matrix defined by $C_{ij} = ⟨δx_iδx_j⟩$, where $δx$ is the distance of a particle from the centroid $x$. $C$ is symmetric so only counts as 6 elements of the overall vector. $V$ is a general 3 × 3 matrix that determines the velocity distribution in the bunch by $δ(γv) = Vδx$. In total this makes 6 + 6 + 9 = 21 elements.

43 PARTICLE ACCELERATORS↗

DOE OSTI2026

Forecasting generative amplification

Generative networks are perfect tools to enhance the speed and precision of LHC simulations. Especially when generating events beyond the size of the training dataset, it is important to understand their statistical precision. We present two complementary methods to estimate the amplification factor without large holdout datasets. Averaging amplification uses Bayesian networks or ensembling to estimate amplification from the precision of integrals over given phase-space volumes. Differential amplification uses hypothesis testing to quantify amplification without any resolution loss. Applied to state-of-the-art event generators, both methods indicate that amplification is already possible in specific regions of phase space.

Bahl, Henning [Heidelberg Univ. (Germany)] (ORCID:↗

DOE OSTI2025

Measurement of the inclusive WZ production cross section in pp collisions at $\sqrt{\textrm{s}}$ = 13.6 TeV

The inclusive WZ production cross section is measured in proton-proton collisions at a centre-of-mass energy of 13.6 TeV, using data collected during 2022 with the CMS detector, corresponding to an integrated luminosity of 34.7 fb −1 . The measurement uses multileptonic final states and a simultaneous likelihood fit to the number of events in four different lepton flavour categories: eee, ee μ , μμ e, and μμμ . The selection is optimized to minimize the number of background events, and relies on an efficient prompt lepton discrimination strategy. The WZ production cross section is measured in a phase space defined within a 30 GeV window around the Z boson mass, as σ total (pp → WZ) = 55.2 ± 1.2 (stat) ± 1.2 (syst) ± 0.8 (lumi) ± 0.3 (theo) pb. In addition, the cross section is measured in a fiducial phase space closer to the detector-level requirements. All the measurements presented in this paper are in agreement with standard model predictions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Measurement of three-dimensional inclusive muon-neutrino charged-current cross sections on argon with the MicroBooNE detector

We report the measurement of the triple-differential cross section d 3 σ/dE vis d cos(θ μ )dP μ for inclusive muon-neutrino charged-current scattering on argon. This measurement utilizes data from 6.4 x 10 20 protons on target of exposure collected using the MicroBooNE liquid argon time projection chamber located along the Fermilab Booster Neutrino Beam with a mean neutrino energy of approximately 0.8 GeV. The mapping from reconstructed kinematics to truth quantities is validated within uncertainties by comparing the distribution of reconstructed hadronic energy in data to that of the model prediction in different muon scattering angle bins after applying a conditional constraint from the muon momentum distribution in data. The success of this validation provides confidence that the energy transfer in the MicroBooNE detector is well-modeled within simulation uncertainties, enabling a reliable unfolding to a triple-differential cross section defined at the nominal neutrino flux over muon momentum, muon scattering angle, and visible neutrino energy. This validation not only supports accurate cross-section extraction, but also establishes a critical foundation for tuning interaction models used in future neutrino oscillation measurements. The unfolded measurement covers an extensive phase space, providing a wealth of information useful for future liquid argon time projection chamber experiments measuring neutrino oscillations. Comparisons against a number of commonly used model predictions are included and their performance in different parts of the available phase-space is discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Giant quantum oscillations in thermal transport in low-density metals via electron absorption of phonons

Oscillations of conductance observed in strong magnetic fields are a striking manifestation of the quantum dynamics of charge carriers in solids. The large charge carrier density in typical metals sets the scale of oscillations in both electrical and thermal conductivity, which characterize the Fermi surface. In semimetals, thermal transport at low-charge carrier density is expected to be phonon dominated, yet several experiments observe giant quantum oscillations in thermal transport. This raises the question of whether there is an overarching mechanism leading to sizable oscillations that survives in phonon-dominated semimetals. In this work, we show that such a mechanism exists. It relies on the peculiar phase-space allowed for phonon scattering by electrons when only a few Landau levels are filled. Our measurements on the Dirac semimetal ZrTe 5 support this counterintuitive mechanism through observation of pronounced thermal quantum oscillations, since they occur in similar magnitude and phase in directions parallel and transverse to the magnetic field. Our phase-space argument applies to all low-density semimetals, topological or not, including graphene and bismuth. Our work illustrates that phonon absorption can be leveraged to reveal degrees of freedom through their imprint on longitudinal thermal transport.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

A projection method for particle resampling

Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase-space due to their better scalability than continuum approaches with respect to dimension. Complex processes collectively referred to as particle noise hamper long time simulations with particle methods. One approach to address this problem is particle mesh adaptivity, or remapping, known as particle resampling and remeshing. Here, this work introduces a resampling method that projects particles to and from a (finite element) function space. The method is simple, using standard sparse linear algebra and finite element techniques, and it preserves all moments up to the order of a polynomial represented exactly by the continuum function space. It is distinguished from most other mesh-based methods in that new particle positions and number are decoupled from the mesh, allowing particle and continuum meshes to be adapted relatively independently. While this work is developed with structured particle and continuum phase-space grids on 1X + 1V Vlasov-Poisson models of Landau damping and two-stream instability, the method is well-suited to unstructured grids. Stable long time dynamics are demonstrated up to time T = 500. Reproducibility artifacts and data are publicly available.

Kinetic methods↗

DOE OSTI2026

Transverse Kinematic Imbalance in MicroBooNE's New nue CC0pi Measurements

Neutrino-nucleus cross section measurements require accurate modelling of neutrino interactions. Neutrino beams are not monoenergetic, and the energy of each interaction must instead be modelled using nuclear interaction assumptions. This introduces significant systematic uncertainty into cross section measurements. Effects such as Fermi motion, nuclear correlations, and final-state interactions (FSI) smear the underlying quasi-elastic scattering signal, making it difficult to disentangle genuine quasi-elastic kinematics from nuclear effects across the full range of interaction channels (QE, MEC, RES, DIS) probed in these measurements. Transverse Kinematic Imbalance (TKI) variables, such as $\delta p_T$ and $\delta \alpha_T$, probe this same phase space by exploiting the fact that the incoming neutrino has zero transverse momentum ($\vec{p}_T^{\,\nu} = 0$). Any measured transverse imbalance in the final state therefore arises from nuclear effects rather than from uncertainty in the incident neutrino energy, allowing cross section measurements to select a phase space that is rich in quasi-elastic-like events with minimal contamination from FSI and other nuclear effects, independent of energy reconstruction. Recent unfolded MicroBooNE cross section measurements of electron-neutrino charged-current interactions with zero pions and at least one proton ($\nu_e$ CC0$\pi$, 1eNp0$\pi$) show that several leading nuclear interaction generators (including GENIE variants, NuWro, GiBUU, and NEUT) reproduce the differential cross section in electron energy reasonably well, but consistently struggle to describe the differential cross section in the cosine of the leading proton's angle, yielding lower $p$-values across all seven generators tested. This tension points to a more fundamental, kinematics-driven disagreement between data and generators that is not visible in energy-only cross section observables. This is precisely the regime TKI variables are designed to probe. Following previous TKI cross section measurements with muon-neutrino data in MicroBooNE, this poster presents the case for extending the TKI framework to electron-neutrino cross section measurements as a next step to isolate and characterize the source of the observed generator tension in proton kinematics.

Burridge, Jessica [U. Manchester (main)] (ORCID:00↗

DOE OSTI2026

Third integer resonant extraction transit time simulation studies

In this work, we present the investigation of transit time of particles in the non-linear third-integer resonant extraction process. Transit time is defined as the number of turns a particle takes to get extracted once it is in the unstable region in the phase space, i.e., outside the triangular separatrix in case of third-integer resonance. The study of transit time is important because transit time directly contributes to the beam response time during resonant extraction and thus knowing it apriori would be practically useful in designing of the extraction system. In this work, we shall investigate the analytical derivation of the transit time of particles (to the first order Kobayashi Hamiltonian) in different parts of the phase space distribution and compare against the analytical results. We also compare the simulation result of the transit time of particles (with higher statistics) for the static as well as dynamic extraction conditions cases, particularly in the context of resonant extraction parameters for Mu2e experiment at Fermilab.

Narayanan, Aakaash [Fermilab]↗

DOE OSTI2025

Third Integer Resonant Extraction Transit Time Simulation Studies

Narayanan, Aakaash [Fermilab] (ORCID:0000000157944↗

DOE OSTI2024

Measurement of C P Violation Observables in D + → K − K + π + Decays

A search for violation of the charge-parity ( C P ) symmetry in the D + → K − K + π + decay is presented, with proton-proton collision data corresponding to an integrated luminosity of 5.4 fb − 1 , collected at a center-of-mass energy of 13 TeV with the LHCb detector. A novel model-independent technique is used to compare the D + and D − phase-space distributions, with instrumental asymmetries subtracted using the D s + → K − K + π + decay as a control channel. The p value for the hypothesis of C P conservation is 8.1%. The C P asymmetry observables A C P | S ϕ π + = ( 0.95 ± 0.4 3 stat ± 0.2 6 syst ) × 10 − 3 and A C P | S K ¯ * 0 K + = ( − 0.26 ± 0.5 6 stat ± 0.1 8 syst ) × 10 − 3 are also measured. These results show no evidence of C P violation and represent the most sensitive search performed through the phase space of a multibody decay. © 2024 CERN, for the LHCb Collaboration 2024 CERN

Aaij, R. (ORCID:0000000305331952)↗

DOE OSTI2025

Confined and deconfined chaos in classical spin systems

Weakly perturbed integrable many-body systems are typically chaotic, and thermal at late times. However, there are distinct relationships between the timescales for thermalization and chaos. The typical relationship is confined chaos: when trajectories are still confined to regions in phase space with constant conserved quantities (actions), the conjugate angle variables are already unstable. Chaotic instabilities thus far precede thermalization. In a different relationship, which we term deconfined chaos, chaotic instabilities and thermalization occur on the same timescale. We investigate these two qualitatively distinct scenarios through numerical and analytical studies of two perturbed integrable classical spin models: the Ishimori spin chain (confined chaos), and the central spin model with XX interactions (deconfined chaos). We analytically establish (super)-integrability in the latter model in a microcanonical shell. Deconfined chaos emerges through the separation of phase space into large quasi-integrable regions and a thin chaotic manifold. The latter leads to chaos and thermalization on the fastest possible timescale, which is proportional to the inverse perturbation strength. This behavior is reminiscent of the quantum SYK models and strange metals.

Chaotic Dynamics (nlin.CD)↗

DOE OSTI2025

Dark Matter Velocity Distributions for Direct Detection: Astrophysical Uncertainties Are Smaller Than They Appear

The sensitivity of direct detection experiments depends on the phase-space distribution of dark matter near the Sun, which can be modeled theoretically using cosmological hydrodynamical simulations of Milky Way–like galaxies. However, capturing the halo-to-halo variation in the local dark matter speeds—a necessary step for quantifying the astrophysical uncertainties that feed into experimental results—requires a sufficiently large sample of simulated galaxies, which has been a challenge. In this Letter, we quantify this variation with nearly 100 Milky Way–like galaxies from the tng50 simulation, the largest sample to date at this resolution. Moreover, we introduce a novel phase-space scaling procedure that endows every system with a reference frame that accurately reproduces the local standard-of-rest speed of our Galaxy, providing a principled way of extrapolating the simulation results to real-world data. The ensemble of predicted speed distributions is well characterized by the standard halo model, a Maxwell-Boltzmann distribution truncated at the escape speed, though the individual distributions can deviate from it, especially at high speeds. The dark matter–nucleon cross section limits placed by these speed distributions vary by ∼ 60% about the median. This places the 1⁢𝜎 astrophysical uncertainty at or below the level of the systematic uncertainty of current ton-scale detectors, even down to the energy threshold. The predicted uncertainty remains unchanged when subselecting on those TNG 50 galaxies with merger histories similar to the Milky Way. Tabulated speed distributions, as well as Maxwell-Boltzmann fits, are provided for use in computing direct detection bounds or projecting sensitivities.

Milky Way↗

DOE OSTI2024

Measurement of top-quark pair production in association with charm quarks in proton–proton collisions at √s = 13 TeV with the ATLAS detector

Inclusive cross-sections or top-quark pair production in association with charm quarks are measured with proton-proton collision data at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of 140 fb -1 , collected with the ATLAS experiment at LHC between 2015 and 2018. The measurements are performed by requiring one or two charged leptons (electrons and muons), two b-tagged jets, and at least one additional jet in the final state. A custom flavor-tagging algorithm is employed for the simultaneous identification of b-jets and c-jets. In a fiducial phase space that replicates the acceptance of the ATLAS detector, the cross-sections for $t\bar{t}$ + ≥ 2c and $t\bar{t}$ + 1c production are measured to be $1.28^{+0.27}_{-0.24}$ pb and $6.4^{+1.0}_{-0.9}$ pb, respectively. The measurements are primarily limited by uncertainties in the modeling of inclusive $t\bar{t}$ and $t\bar{t}$ + $b\bar{b}$ production, in the calibration of the flavor-tagging algorithm, and by data statistics. Cross-section predictions from various $t\bar{t}$ simulations are largely consistent with the measured cross-section values, though all underpredict the observed values by 0.5 to 2.0 standard deviations. In a phase-space volume without requirements on the $t\bar{t}$ decay products and the jet multiplicity, the cross-section ratios of $t\bar{t}$ + ≥ 2c and $t\bar{t}$ + 1c to total $t\bar{t}$ + jets production are determined to be (1.23 ± 0.25)% and (8.8 ± 1.3)%.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Regulation of Solar Wind Electron Temperature Anisotropy by Collisions and Instabilities

Abstract Typical solar wind electrons are modeled as being composed of a dense but less energetic thermal “core” population plus a tenuous but energetic “halo” population with varying degrees of temperature anisotropies for both species. In this paper, we seek a fundamental explanation of how these solar wind core and halo electron temperature anisotropies are regulated by combined effects of collisions and instability excitations. The observed solar wind core/halo electron data in ( β ∥ , T ⊥ / T ∥ ) phase space show that their respective occurrence distributions are confined within an area enclosed by outer boundaries. Here, T ⊥ / T ∥ is the ratio of perpendicular and parallel temperatures and β ∥ is the ratio of parallel thermal energy to background magnetic field energy. While it is known that the boundary on the high- β ∥ side is constrained by the temperature anisotropy-driven plasma instability threshold conditions, the low- β ∥ boundary remains largely unexplained. The present paper provides a baseline explanation for the low- β ∥ boundary based upon the collisional relaxation process. By combining the instability and collisional dynamics it is shown that the observed distribution of the solar wind electrons in the ( β ∥ , T ⊥ / T ∥ ) phase space is adequately explained, both for the “core” and “halo” components.

Yoon, Peter H. (ORCID:0000000181343790)↗

DOE OSTI2026

Experimental longitudinal emittance manipulation using laser-based photoionization in the Fermilab Linac

A series of simulations and beam studies were conducted at Fermilab’s linear accelerator to evaluate the effectiveness of longitudinal emittance control via laser-induced photoionization. While similar laser techniques have been employed at Fermilab to enhance injection and extraction efficiency into the Booster, the work presented here focuses on extending these methods to bunch-by-bunch manipulation. This approach utilizes fine-scale correction of the H- bunches’ longitudinal spatial distribution. In theory, loosely confined particles in longitudinal phase space contribute to emittance growth during acceleration. By selectively removing these outlying particles through laser scraping (H- + γ → H + e-), this growth can be reduced. This report presents experimental results from both symmetric and asymmetric longitudinal scraping of H⁻ bunches in the Fermilab linac, which were subsequently injected into Booster, and evaluates the broader applicability of this method for future high-intensity accelerator operations.

Landon, Parker [Boston U.; Fermilab]↗