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Results for “PHASE-SPACE INTEGRAL”

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

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Double-real corrections to color singlet decay in a parton-shower inspired scheme

We introduce a local infrared subtraction method for next-to-next-to-leading order QCD calculations in color singlet decays, with counterterms based on scalar radiators and pure splitting functions. Overlapping singularities in the multipole radiation pattern are disentangled by partial fractioning, and the kinematics mapping corresponds to iterated next-to-leading order kinematics. We verify that the double-real remainder to $e^+e^-\to\;q\bar{q}$ is rendered finite in the single and double unresolved limits and investigate the numerical convergence of the Monte-Carlo integral. We compute the phase-space integrals of the scalar counterterms in the back-to-back configuration, both analytically and with the help of numerical techniques based on sector decomposition.

Campbell, John M. [Fermilab]↗
NASA NTRS1992

Squeezed states and path integrals

The continuous-time regularization scheme for defining phase-space path integrals is briefly reviewed as a method to define a quantization procedure that is completely covariant under all smooth canonical coordinate transformations. As an illustration of this method, a limited set of transformations is discussed that have an image in the set of the usual squeezed states. It is noteworthy that even this limited set of transformations offers new possibilities for stationary phase approximations to quantum mechanical propagators.

Daubechies, Ingrid↗
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:↗
NASA NTRS1988

Computer modeling of test particle acceleration at oblique shocks

The present evaluation of the basic techniques and illustrative results of charged particle-modeling numerical codes suitable for particle acceleration at oblique, fast-mode collisionless shocks emphasizes the treatment of ions as test particles, calculating particle dynamics through numerical integration along exact phase-space orbits. Attention is given to the acceleration of particles at planar, infinitessimally thin shocks, as well as to plasma simulations in which low-energy ions are injected and accelerated at quasi-perpendicular shocks with internal structure.

Decker, Robert B.↗
DOE OSTI2025

Cosmic structure strikes back: The elimination of vector-mediated nonstandard interaction models as a mechanism for sterile neutrino dark matter production

We revisit sterile neutrino production enabled by nonstandard interactions (NSIs) among active neutrinos mediated by new bosons. We focus on vector mediators, including neutrinophilic, gauged 𝐿 𝜇 −𝐿 𝜏 , and 𝐵−𝐿 realizations, that modify in-medium dispersion and scattering, thereby altering the active-sterile conversion history. Building on a novel production framework with NSI thermal potentials and collision integrals, we compute nonthermal phase-space distributions across sterile neutrino mixing and NSI parameters and map each point to an equivalent thermal warm dark matter particle mass 𝑚 th via linear theory transfer function fitting with the cosmological structure formation Boltzmann solver. This enables a direct reinterpretation of state-of-the-art structure formation limits from Milky Way satellites, strong lensing, and the Lyman-𝛼 forest. These limits, in conjunction with x-ray decay searches, as well as results from a wide variety of particle physics experiments allow for a more complete examination of these models. We find that these vector-mediated models are ruled out when the full combination of current constraints, listed above, are taken into account. NSI scalar-mediated models and models with low reheating temperatures remain viable.

cosmology↗
NASA NTRS1976

Kinetic theory of turbulent compressible flows and comparison with classical theory

A complete set of turbulent correlations is given in terms of expansion coefficients in a double series of Hermite polynomials of a two-particle correlation in phase space. Only two of these coefficients, corresponding to Reynolds stress and turbulent heat flux, are shown to appear in gasdynamic equations of turbulence. This is accomplished by incorporating the phase-space correlation in the collision integral of Boltzmann's equation and by deriving generalized Navier-Stokes and Fourier transport relations. In contrast to the classical formalism, the simple expression remains invariant in form whether the flow is compressible or not. Nevertheless, a bilinear transformation of fluctuating quantities shows that the two formalisms are identical with regard to terms of double correlations. The kinetic theory justifies nonexistence of the higher-order correlations characteristic of compressible-turbulence equations in the classical regime.

Tsuge, S.↗
DOE OSTI2026

A Monte Carlo Laplace Transform Estimator for Radiation Transport

This work formulates and implements a Laplace transform estimator in a simple Monte Carlo radiation transport code. The estimator maps flux-based quantities of interest, like reaction rates, from a desired phase-space dimension to the complex Laplace domain. This on-the-fly Monte Carlo integration technique enables the spectral analysis of arbitrary nuclear systems via the Laplace transform. A simple code tests the estimator in neutron slowing-down problems across various infinite media, and the results compare well with Ganapol’s uninverted analytical solution of the neutron slowing-down equation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Symplectic machine learning model for fast simulation of space-charge effects

Symplectic simulation of space-charge effects is crucial for the design and operation of high-intensity particle accelerators. Traditional methods for simulating these effects are often computationally expensive, resulting in significant overhead. In this work, we introduce a generative model based on a U-Net architecture within a generative adversarial network framework to efficiently simulate space-charge effects. The model is trained to predict the transverse multiparticle space-charge Hamiltonian, which can be physically computed using a gridless spectral method. The one-step symplectic transverse transfer map for the particles is then obtained by differentiating the predicted Hamiltonian. Benchmarking results demonstrate that this generative model achieves an order of magnitude higher computational efficiency compared to the spectral method, providing a highly efficient alternative for simulating space-charge effects with a large number of particles. By maintaining symplecticity, the model effectively preserves the phase-space structure and mitigates nonphysical errors in long-term simulations. This model has been integrated into jutrack, a novel autodifferentiable accelerator modeling code developed in the julia programming language.

Beam code development & simulation techniques↗
DOE OSTI2025

Dynamics of McMillan mappings I. McMillan multipoles

In this article, we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings, originally proposed by Edwin McMillan. Both represent the simplest symmetric McMillan maps, characterized by a single intrinsic parameter. While these systems find numerous applications across various domains of mathematics and physics, some of their dynamical properties remain unexplored. We aim to bridge this gap by providing a comprehensive description of all stable trajectories, including the parametrization of invariant curves, Poincaré rotation numbers, and canonical action–angle variables. In the second part, we establish connections between these maps and general chaotic maps in standard form. Our investigation reveals that the McMillan sextupole and octupole serve as first-order approximations of the dynamics around the fixed point, akin to the linear map and quadratic invariant (known as the Courant–Snyder invariant in accelerator physics), which represents zeroth-order approximations (referred to as linearization). Furthermore, we propose a novel formalism for nonlinear Twiss parameters, which accounts for the dependence of rotation number on amplitude. This stands in contrast to conventional betatron phase advance used in accelerator physics, which remains independent of amplitude. Notably, in the context of accelerator physics, this new formalism demonstrates its capability in predicting dynamical aperture around low-order resonances for flat beams, a critical aspect in beam injection/extraction scenarios.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

ELG×LRG Distribution through Dark Matter Halo Dynamics

We investigate the clustering and halo occupation distribution (HOD) of DESI Y1 emission-line (ELGs) and luminous red (LRGs) galaxies at 0.8 < z < 1.1, including their cross-correlation (ELG×LRG), using the A BACUS S UMMIT suite and a new Halo Occupation Model (H OME ) for galaxy multitracers. This integrates intrahalo dynamics, halo exclusion, and quenching, bridging insights from hydrodynamical, HOD, abundance-matching, and semianalytic studies. Leveraging full phase-space information from the Uchuu N-body simulation, and sampling satellites from dark-matter particle positions via physically motivated prescriptions, Home reproduces the anisotropic clustering down to s = 200 h −1 kpc with unprecedented accuracy. Model parameters are inferred solely from two-point statistics using a two-level Bayesian framework, yielding high-fidelity ELG, LRG, and cross-reference catalogs. We find that satellite ELGs behave as incoherent flows within their parent halos, dominating the clustering below 4 h −1 Mpc. The HOD from the best-fit Home has the following properties: (i) 90.50% (85.91%) of ELGs (LRGs) are central galaxies without satellites, residing in halos of M vir ∼ 6.6 × 10 11 (1.2 × 10 13 ) h −1 M ⊙ ; (ii) the ELG×LRG cross-correlation is governed by central-central pairs and shaped by halo exclusion on 2–5 h −1 Mpc scales; (iii) 9.50% (14.09%) of ELGs (LRGs) are satellites, of which 1.09% (3.52%) inhabit halos with a central galaxy of the same species in a maximally conformal configuration, 7.02% (0.005%) orbit complementary hosts in a minimally conformal state, and 0.58% (10.57%) are orphans. The high sensitivity of Home precisely captures the dynamics of satellites in different host environments, opening a promising avenue for understanding systematics and the dynamical nature of dark matter, potentially distinguishing gravity models.

Favole, Ginevra [Universidad de La Laguna (Spain);↗
DOE OSTI2026

Velocity-space Origins of the Pressure–Strain Interaction in Multipopulation Distributions and Its Application to Magnetic Reconnection

A forefront research question is how energy evolves in weakly collisional plasmas for which departures from local thermodynamic equilibrium (LTE) are significant. The standard approach is studying the terms in the non-LTE energy evolution equation derived by taking the second moment of the Boltzmann equation, but the resultant fluid metrics do not retain information about which particles at which velocities drive energy evolution. A widely studied channel for internal energy density evolution is the pressure–strain interaction. Here, we employ the kinetic pressure–strain, a phase-space diagnostic whose velocity-space integral recovers the pressure–strain interaction to disambiguate the contributions to the pressure–strain interaction from disparate particle populations in composite phase-space densities. We develop phase-space analogs of the pressure–strain interaction decompositions to provide the phase-space origins of normal versus sheared flow. We introduce the “kinetic strain-rate” tensor, the phase-space analog of the strain-rate tensor, which we argue is needed to interpret the phase-space origins of the pressure–strain interaction. To demonstrate the utility of these quantities, we investigate them for composite electron distributions near the electron diffusion region in two-dimensional particle-in-cell simulations of antiparallel symmetric magnetic reconnection. We find that the phase-space-based diagnostics isolate the roles of distinct populations. These results contribute to a growing body of work providing new methods for quantifying phase-space energy evolution for a broad array of processes, from magnetic reconnection to collisionless shocks and turbulence, opening new pathways for answering longstanding problems of particle energization in weakly collisional plasmas.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Realizability-preserving discontinuous Galerkin method for spectral two-moment radiation transport in special relativity

Here we present a realizability-preserving numerical method for solving a spectral two-moment model to simulate the transport of massless, neutral particles interacting with a steady background material moving with relativistic velocities. The model is obtained as the special relativistic limit of a four-momentum-conservative general relativistic two-moment model. Using a maximum-entropy closure, we solve for the Eulerian-frame energy and momentum. The proposed numerical method is designed to preserve moment realizability, which corresponds to moments defined by a nonnegative phase-space density. The realizability-preserving method is achieved with the following key components: (i) a discontinuous Galerkin phase-space discretization with specially constructed numerical fluxes in the spatial and energy dimensions; (ii) a strong stability-preserving implicit-explicit time-integration method; (iii) a realizability-preserving conserved to primitive moment solver; (iv) a realizability-preserving implicit collision solver; and (v) a realizability-enforcing limiter. Component (iii) is necessitated by the closure procedure, which closes higher order moments nonlinearly in terms of primitive moments. The nonlinear conserved to primitive and the implicit collision solves are formulated as fixed-point problems, which are solved with custom iterative solvers designed to preserve the realizability of each iterate. With a series of numerical tests, we demonstrate the accuracy and robustness of this discontinuous-Galerkin-implicit-explicit method.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1992

Polynomial approximation of Poincare maps for Hamiltonian system

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Froeschle, Claude↗
DOE OSTI2025

Dynamics of McMillan mappings II. axially symmetric map

Here, in this article, we investigate the transverse dynamics of a single particle in a model integrable accelerator lattice, based on a McMillan axially-symmetric electron lens. Although the McMillan e-lens has been considered as a device potentially capable of mitigating collective space charge forces, some of its fundamental properties have not been described yet. The main goal of our work is to close this gap and understand the limitations and potentials of this device. It is worth mentioning that the McMillan axially symmetric map provides the first-order approximations of dynamics for a general linear lattice plus an arbitrary thin lens with motion separable in polar coordinates. Therefore, advancements in its understanding should give us a better picture of more generic and not necessarily integrable round beams. In the first part of the article, we classify all possible regimes with stable trajectories and find the canonical action-angle variables. This provides an evaluation of the dynamical aperture, Poincaré rotation numbers as functions of amplitudes, and thus determines the spread in nonlinear tunes. Also, we provide a parameterization of invariant curves, allowing for the immediate determination of the map image forward and backward in time. The second part investigates the particle dynamics as a function of system parameters. We show that there are three fundamentally different configurations of the accelerator optics causing different regimes of nonlinear oscillations. Each regime is considered in great detail, including the limiting cases of large and small amplitudes. In addition, we analyze the dynamics in Cartesian coordinates and provide a description of observable variables and corresponding spectra.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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)↗
NASA NTRS1989

Qualitative simulation for process modeling and control

A qualitative model is developed for a first-order system with a proportional-integral controller without precise knowledge of the process or controller parameters. Simulation of the qualitative model yields all of the solutions to the system equations. In developing the qualitative model, a necessary condition for the occurrence of oscillatory behavior is identified. Initializations that cannot exhibit oscillatory behavior produce a finite set of behaviors. When the phase-space behavior of the oscillatory behavior is properly constrained, these initializations produce an infinite but comprehensible set of asymptotically stable behaviors. While the predictions include all possible behaviors of the real system, a class of spurious behaviors has been identified. When limited numerical information is included in the model, the number of predictions is significantly reduced.

Dalle Molle, D. T.↗