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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 199 records · Page 11
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DOE OSTI2024

Anderson acceleration with approximate calculations: Applications to scientific computing

Here we provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the convergence of AA is maintained while the computational time could be reduced. We also provide computable heuristic quantities, guided by the theoretical error bounds, which can be used to automate the tuning of accuracy while performing approximate calculations. For linear problems, the use of heuristics to monitor the error introduced by approximate calculations, combined with the check on monotonicity of the residual, ensures the convergence of the numerical scheme within a prescribed residual tolerance. Motivated by the theoretical studies, we propose a reduced variant of AA, which consists in projecting the least-squares used to compute the Anderson mixing onto a subspace of reduced dimension. The dimensionality of this subspace adapts dynamically at each iteration as prescribed by the computable heuristic quantities. We numerically show and assess the performance of AA with approximate calculations on: (i) linear deterministic fixed-point iterations arising from the Richardson's scheme to solve linear systems with open-source benchmark matrices with various preconditioners and (ii) non-linear deterministic fixed-point iterations arising from non-linear time-dependent Boltzmann equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Correlating processing variables to material properties in recycled polypropylene: A data‐driven approach

Abstract Polypropylene (PP) is one of the most widely used plastics, yet its recycling remains limited, with less than 1% of solid waste PP being reprocessed. Mechanical recycling through extrusion is the most practical method, but inconsistent reprocessing conditions introduce variability in material properties. While temperature, screw speed, and residence time influence the thermomechanical stress applied during reprocessing, there are no standardized guidelines for optimizing these parameters. This study examines how these factors shape the properties of recycled PP, using conditions designed to mimic post‐industrial recycled (PIR) scrap. Residence time was measured using colorimetric tracking and correlated with molecular weight, viscosity, and mechanical properties over multiple extrusion cycles. Data‐driven modeling, including response surface methodology, support vector machines, and artificial neural networks, identified processing temperature as the dominant factor in material degradation, followed by residence time. Mechanical properties remained stable, while viscosity decreased predictably with increasing residence time. By linking reprocessing conditions to property evolution, this study provides a method to optimize processing parameters and reduce variability in recycled PP. These findings help manufacturers improve process control, making recycled PP more predictable for reuse in manufacturing. Highlights Study of PIR‐quality PP without additives or compatibilizers. Residence time analysis shows processing temperature drives PP property changes. Mark‐Houwink enables quick molecular weight checks for quality control. Models predict mechanical and rheological shifts in reprocessing. Optimized processing parameters minimize property degradation in recycling.

Estela‐García, John E. [Polymer Engineering Center↗
DOE OSTI2021

Positive geometry, local triangulations, and the dual of the Amplituhedron

We initiate the systematic study of local positive spaces which arise in the context of the Amplituhedron construction for scattering amplitudes in planar maximally supersymmetric Yang-Mills theory. We show that all local positive spaces relevant for one-loop MHV amplitudes are characterized by certain sign-flip conditions and are associated with surprisingly simple logarithmic forms. In the maximal sign-flip case they are finite one-loop octagons. Particular combinations of sign-flip spaces can be glued into new local positive geometries. These correspond to local pentagon integrands that appear in the local expansion of the MHV one-loop amplitude. We show that, geometrically, these pentagons do not triangulate the original Amplituhedron space but rather its twin “Amplituhedron-Prime”. This new geometry has the same boundary structure as the Amplituhedron (and therefore the same logarithmic form) but differs in the bulk as a geometric space. On certain two-dimensional boundaries, where the Amplituhedron geometry reduces to a polygon, we check that both spaces map to the same dual polygon. Interestingly, we find that the pentagons internally triangulate that dual space. This gives a direct evidence that the chiral pentagons are natural building blocks for a yet-to-be discovered dual Amplituhedron.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Sequential discontinuities of Feynman integrals and the monodromy group

We generalize the relation between discontinuities of scattering amplitudes and cut diagrams to cover sequential discontinuities (discontinuities of discontinuities) in arbitrary momentum channels. The new relations are derived using time-ordered perturbation theory, and hold at phase-space points where all cut momentum channels are simultaneously accessible. As part of this analysis, we explain how to compute sequential discontinuities as monodromies and explore the use of the monodromy group in characterizing the analytic properties of Feynman integrals. We carry out a number of cross-checks of our new formulas in polylogarithmic examples, in some cases to all loop orders.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Yang-Mills observables: from $\mathrm{KMOC}$ to eikonal through $\mathrm{EFT}$

We obtain a conservative Hamiltonian describing the interactions of two charged bodies in Yang-Mills through $\mathcal{O}$ (α 2 ) and to all orders in velocity. Our calculation extends a recently-introduced framework based on scattering amplitudes and effective field theory (EFT) to consider color-charged objects. These results are checked against the direct integration of the observables in the Kosower-Maybee-O’Connell (KMOC) formalism. At the order we consider we find that the linear and color impulses in a scattering event can be concisely described in terms of the eikonal phase, thus extending the domain of applicability of a formula originally proposed in the context of spinning particles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Threshold resummation for double-deeply virtual Compton scattering

The threshold region for double-deeply virtual Compton scattering (DDVCS) is discussed. I derive a resummation formula for the (partonic) threshold logarithms in the flavor non-singlet case. The resummations can be done by using (re)factorization theorems for the coefficient functions near the partonic thresholds. As a byproduct, we obtain the leading term in the threshold limit of the two-loop coefficient function in double-deeply-virtual Compton scattering, which agrees with the recent result from explicit calculation, providing a highly non-trivial cross-check.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Updated constraints from electric dipole moments in the MSSM with R-parity violation

We revisit the electric dipole moments (EDMs) of quarks and leptons in the Minimal Supersymmetric Standard Model (MSSM) with trilinear R-parity violation (RPV). In this framework, EDMs are induced at the two-loop level via RPV interactions. We perform a comprehensive recalculation of several classes of Barr-Zee type diagrams in a general Rξ gauge. While we find general agreement with previous analytic results in the literature, our work provides a valuable independent cross-check of the complicated calculations. We also point out some subtleties in the intermediate steps and in the choice of the flavor basis for the numerical evaluation of the expressions. By confronting the theoretical predictions with the latest experimental limits on EDMs, we derive updated constraints on combinations of RPV couplings. We highlight an approximate, testable correlation between the proton and neutron EDM that emerges within the considered class of RPV models, offering a distinctive signature for future EDM experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Heterotic instantons for monad and extension bundles

We consider non-perturbative superpotentials from world-sheet instantons wrapped on holomorphic genus zero curves in heterotic string theory. These superpotential contributions feature prominently in moduli stabilization and large field axion inflation, which makes their presence or absence, as well as their functional dependence on moduli, an important issue. We develop geometric methods to compute the instanton superpotentials for heterotic string theory with monad and extension bundles. Using our methods, we find a variety of examples with a non-vanishing superpotential. In view of standard vanishing theorems, we speculate that these results are likely to be attributed to the non-compactness of the instanton moduli space. We test this proposal, for the case of monad bundles, by considering gauged linear sigma models where compactness of the instanton moduli space can be explicitly checked. In all such cases, we find that the geometric results are consistent with the vanishing theorems. Surprisingly, linearly dependent Pfaffians even arise for cases with a non-compact instanton moduli space. This suggests some gauged linear sigma models with a non-compact instanton moduli space may still have a vanishing instanton superpotential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)

We recently introduced in [9] a boundary-to-bound dictionary between gravitational scattering data and observables for bound states of non-spinning bodies. In this paper, we elaborate further on this holographic map. We start by deriving the following — remarkably simple — formula relating the periastron advance to the scattering angle: $ΔΦ(J,ε)=χ(J,ε)+χ(-J,ε)$, via analytic continuation in angular momentum and binding energy. Using explicit expressions from [9], we confirm its validity to all orders in the Post-Minkowskian (PM) expansion. Furthermore, we reconstruct the radial action for the bound state directly from the knowledge of the scattering angle. The radial action enables us to write compact expressions for dynamical invariants in terms of the deflection angle to all PM orders, which can also be written as a function of the PM-expanded amplitude. As an example, we reproduce our result in [9] for the periastron advance, and compute the radial and azimuthal frequencies and redshift variable to two-loops. Agreement is found in the overlap between PM and Post-Newtonian (PN) schemes. Last but not least, we initiate the study of our dictionary including spin. We demonstrate that the same relation between deflection angle and periastron advance applies for aligned-spin contributions, with J the (canonical) total angular momentum. Explicit checks are performed to display perfect agreement using state-of-the-art PN results in the literature. Using the map between test- and two-body dynamics, we also compute the periastron advance up to quadratic order in spin, to one-loop and to all orders in velocity. We conclude with a discussion on the generalized ‘impetus formula’ for spinning bodies and black holes as ‘elementary particles’. Our findings here and in [9] imply that the deflection angle already encodes vast amount of physical information for bound orbits, encouraging independent derivations using numerical and/or self-force methodologies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Perfecting one-loop BCJ numerators in SYM and supergravity

We take a major step towards computing D-dimensional one-loop amplitudes in general gauge theories, compatible with the principles of unitarity and the color-kinematics duality. For n-point amplitudes with either supersymmetry multiplets or generic non-supersymmetric matter in the loop, simple all-multiplicity expressions are obtained for the maximal cuts of kinematic numerators of n-gon diagrams. At n = 6, 7 points with maximal supersymmetry, we extend the cubic-diagram numerators to encode all contact terms, and thus solve the long-standing problem of simultaneously realizing the following properties: color-kinematics duality, manifest locality, optimal power counting of loop momenta, quadratic rather than linearized Feynman propagators, compatibility with double copy as well as all graph symmetries. Color-kinematics dual representations with similar properties are presented in the half-maximally supersymmetric case at n = 4, 5 points. The resulting gauge-theory integrands and their supergravity counterparts obtained from the double copy are checked to reproduce the expected ultraviolet divergences.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Exact quantization and analytic continuation

In this paper we give a streamlined derivation of the exact quantization condition (EQC) on the quantum periods of the Schrödinger problem in one dimension with a general polynomial potential, based on Wronskian relations. We further generalize the EQC to potentials with a regular singularity, describing spherical symmetric quantum mechanical systems in a given angular momentum sector. We show that the thermodynamic Bethe ansatz (TBA) equations that govern the quantum periods undergo nontrivial monodromies as the angular momentum is analytically continued between integer values in the complex plane. The TBA equations together with the EQC are checked numerically against Hamiltonian truncation at real angular momenta and couplings, and are used to explore the analytic continuation of the spectrum on the complex angular momentum plane in examples.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Analyticity of replica correlators and modular ETH

We study the two point correlation function of a local operator on an n -sheeted replica manifold corresponding to the half-space in the vacuum state of a conformal field theory. In analogy with the inverse Laplace transform, we define the Renyi transform of this correlation function, which is a function of one complex variable w, dual to the Renyi parameter n . Inspired by the inversion formula of Caron-Huot, we argue that if the Renyi transform ƒ(w) has bounded behavior at infinity in the complex w plane, the discontinuity of the Renyi transform disc ƒ(w) provides the unique analytic continuation in n of the original replica correlation function. We check our formula by explicitly calculating the Renyi transform of a particular replica correlator in a large N holographic CFT d in dimensions d > 2. We also discover that the discontinuity of the Renyi transform is related to the matrix element of local operators between two distinct eigenstates of the modular Hamiltonian. We calculate the Renyi transform in 2 d conformal field theories, and use it to extract the off-diagonal elements of (modular) ETH. We argue that in 2 d , this is equivalent to the off-diagonal OPE coefficients of a CFT and show that our technique exactly reproduces recent results in the literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

LSZ in action: extracting form factors from correlators nonperturbatively in 2d ϕ4 theory

Abstract In this paper, we compute multiparticle form factors of local operators in 2dϕ 4 theory using a recently proposed method [1] for efficiently implementing the LSZ prescription with Hamiltonian Truncation methods, and we adopt Lightcone Conformal Truncation (LCT) in particular for our calculations. We perform various checks of our results at weak and strong coupling, and elucidate the parametric behavior of truncation errors. This opens up the possibility to compute S-matrix in various strongly coupled models using the LSZ method in LCT.

Physics↗
DOE OSTI2020

General F-theory models with tuned (SU(3) × SU(2) × U(1))/ Z 6 symmetry

We construct a general form for an F-theory Weierstrass model over a general base giving a 6D or 4D supergravity theory with gauge group (SU(3) × SU(2) × U(1))/Z 6 and generic associated matter, which includes the matter content of the standard model. The Weierstrass model is identified by unHiggsing a model with U(1) gauge symmetry and charges q ≤ 4 previously found by the first author. This model includes two distinct branches that were identified in earlier work, and includes as a special case the class of models recently studied by Cvetič, Halverson, Lin, Liu, and Tian, for which we demonstrate explicitly the possibility of unification through an SU(5) unHiggsing. We develop a systematic methodology for checking that a parameterized class of F-theory Weierstrass models with a given gauge group G and fixed matter content is generic (contains all allowed moduli) and confirm that this holds for the models constructed here.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Factorization connecting continuum & lattice TMDs

Transverse-momentum-dependent parton distribution functions (TMDs) can be studied from first principles by a perturbative matching onto lattice-calculable quantities: so-called lattice TMDs, which are a class of equal-time correlators that includes quasi-TMDs and TMDs in the Lorentz-invariant approach. We introduce a general correlator that includes as special cases these two Lattice TMDs and continuum TMDs, like the Collins scheme. Then, to facilitate the derivation of a factorization relation between lattice and continuum TMDs, we construct a new scheme, the Large Rapidity (LR) scheme, intermediate between the Collins and quasi-TMDs. The LR and Collins schemes differ only by an order of limits, and can be matched onto one another by a multiplicative kernel. We show that this same matching also holds between quasi and Collins TMDs, which enables us to prove a factorization relation between these quantities to all orders in α s . Our results imply that there is no mixing between various quark flavors or gluons when matching Collins and quasi TMDs, making the lattice calculation of individual flavors and gluon TMDs easier than anticipated. We cross-check these results explicitly at one loop and discuss implications for other physical-to-lattice scheme factorizations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Quark and gluon two-loop beam functions for leading-jet p T and slicing at NNLO

We compute the complete set of two-loop beam functions for the transverse momentum distribution of the leading jet produced in association with an arbitrary colour-singlet system. Our results constitute the last missing ingredient for the calculation of the jet-vetoed cross section at small veto scales at the next-to-next-to-leading order, as well as an important ingredient for its resummation to next-to-next-to-next-to-leading logarithmic order. Our calculation is performed in the soft-collinear effective theory framework with a suitable regularisation of the rapidity divergences occurring in the phase-space integrals. We discuss the occurrence of soft-collinear mixing terms that might violate the factorisation theorem, and demonstrate that they are naturally absorbed into the beam functions at two loops in the exponential rapidity regularisation scheme when performing a multipole expansion of the measurement function. As in our recent computation of the two-loop soft function, we present the results as a Laurent expansion in the jet radius R. We provide analytic expressions for all flavour channels in x space with the exception of a set of R-independent non-logarithmic terms that are given as numerical grids. We also perform a fully numerical calculation with exact R dependence, and find that it agrees with our analytic expansion at the permyriad level or better. Our calculation allows us to define a next-to-next-to-leading order slicing method using the leading-jet p T as a slicing variable. As a check of our results, we carry out a calculation of the Higgs and Z boson total production cross sections at the next-to-next-to-leading order in QCD.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Characterizing 4-string contact interaction using machine learning

Abstract The geometry of 4-string contact interaction of closed string field theory is characterized using machine learning. We obtain Strebel quadratic differentials on 4-punctured spheres as a neural network by performing unsupervised learning with a custom-built loss function. This allows us to solve for local coordinates and compute their associated mapping radii numerically. We also train a neural network distinguishing vertex from Feynman region. As a check, 4-tachyon contact term in the tachyon potential is computed and a good agreement with the results in the literature is observed. We argue that our algorithm is manifestly independent of number of punctures and scaling it to characterize the geometry ofn-string contact interaction is feasible.

Physics↗
DOE OSTI2025

Scalar-scaffolded gluons and the combinatorial origins of Yang-Mills theory

We present a new formulation for Yang-Mills scattering amplitudes in any number of dimensions and at any loop order, based on the same combinatorial and binary-geometric ideas in kinematic space recently used to give an all-order description of Tr Φ 3 theory. We propose that in a precise sense the amplitudes for a suitably “stringy” form of these two theories are identical, up to a simple shift of kinematic variables. This connection is made possible by describing the amplitudes for n gluons via a “scalar scaffolding”, arising from the scattering of 2n colored scalars coming in n distinct pairs of flavors fusing to produce the gluons. Fundamental properties of the “u-variables”, describing the “binary geometry” for surfaces appearing in the topological expansion, magically guarantee that the kinematically shifted Tr Φ 3 amplitudes satisfy the physical properties needed to be interpreted as scaffolded gluons. These include multilinearity, gauge invariance, and factorization on tree- and loop-level gluon cuts. Our “stringy” scaffolded gluon amplitudes coincide with amplitudes in the bosonic string for extra-dimensional gluon polarizations at tree-level, but differ (and are simpler) at loop-level. We provide many checks on our proposal, including matching non-trivial leading singularities through two loops. The simple counting problem underlying the u variables autonomously “knows” about everything needed to convert colored scalar to gluon amplitudes, exposing a striking “discovery” of Yang-Mills amplitudes from elementary combinatorial ideas in kinematic space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗