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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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Formal Verification, Distributed Computing, and Path Planning Algorithms

The safety- and mission-critical nature of much of the work done at NASA requires algorithms and software to be exceedingly reliable. Formal methods techniques are one way of ensuring this high level of robustness. This talk will discuss the development and formal verification of autonomous aircraft path planning algorithms related to the Bellman-Ford shortest path algorithm, including consideration of distributed computation of the algorithm.

Formal Methods↗
DOE OSTI2024

Formal Methods for Provably Secure Software and Firmware

This project addresses a gap observed in verifying the programming in embedded devices used in international arms control: namely verifying that embedded programming in an arms control device does exactly what it is supposed to do, no more and no less, every time without fail, and without disclosing unauthorized information accidentally or intentionally. In critical military, aerospace, and industrial safety systems this problem is sometimes addressed using formal methods (FM). This multi-year project seeks to identify formal methods toolsets useable in arms control regimes, with emphasis on applicability, ease of use, long term availability, and support.

formal methods, Arms Control Verification↗
DOE OSTI2023

Spinor-helicity formalism for massive and massless amplitudes in five dimensions

Five-dimensional gauge and gravity theories are known to exhibit striking properties. D = 5 is the lowest dimension where massive tensor states appear naturally, providing a testing ground for perturbative insights into six-dimensional tensor theories. Five-dimensional supergravities are highly constrained and admit elegant geometric and algebraic formulations, with global symmetries manifest at the Lagrangian level. In this paper, we take a step towards the systematic investigation of amplitudes in five dimensions, and present a five-dimensional version of the spinor-helicity formalism, applicable to massless, massive and supersymmetric states. We give explicit representations for on-shell spinor and polarization variables such that the little-group symmetry and gauge redundancy are manifest. Massive self-dual tensor states are discussed in some detail, as well as all the on-shell supermultiplets that can appear in matter-coupled gauge and supergravity theories. As a byproduct of considering supersymmetry in the presence of central charge, we obtain massless ten-dimensional Majorana-Weyl spinors as products of five-dimensional massive spinors. We present compact expressions for superamplitudes at multiplicity three and four, including several novel superamplitudes that either do not straightforwardly uplift to six dimensions, or have not appeared in the six-dimensional literature. We discuss several examples of five-dimensional double-copy constructions in the context of gravitational theories with massive vectors and tensors, illustrating that the formalism we construct can also be used to considerably streamline the double-copy construction of $\mathcal{N}$ = 2 Maxwell-Einstein supergravities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Implementing the finite-volume three-pion scattering formalism across all non-maximal isospins

We present a numerical exploration of the relativistic-field-theory (RFT) formalism for three pions with all possible values of non-maximal isospin, I πππ = 2, 1 and 0. Using the generic-isospin extension of the RFT formalism [1] and applying our open-source Python library to implement the framework, we predict a range of three-pion energies for illustrative values of the two-to-two scattering amplitudes for various finite-volume irreps also with non-zero total momentum P in the finite-volume frame. The results restrict attention to the case of a vanishing intrinsic three-body interaction so that the spectra can be understood as a baseline. In future lattice QCD calculations, deviations from these values will be translated into evidence for intrinsic three-body effects in the various scattering channels.

hadronic spectroscopy↗
DOE OSTI2020

Scattering Observables from One- and Two-body Densities: Formalism and Application to $\pmb \gamma $ ${}^3\hbox {He}$ Scattering

We introduce the transition-density formalism, an efficient and general method for calculating the interaction of external probes with light nuclei. One- and two-body transition densities that encode the nuclear structure of the target are evaluated once and stored. They are then convoluted with an interaction kernel to produce amplitudes, and hence observables. Here, by choosing different kernels, the same densities can be used for any reaction in which a probe interacts perturbatively with the target. The method therefore exploits the factorisation between nuclear structure and interaction kernel that occurs in such processes. We study in detail the convergence in the number of partial waves for matrix elements relevant in elastic Compton scattering on 3 He. The results are fully consistent with our previous calculations in Chiral Effective Field Theory. But the new approach is markedly more computationally efficient, which facilitates the inclusion of more partial-wave channels in the calculation. We also discuss the usefulness of the transition-density method for other nuclei and reactions. Calculations of elastic Compton scattering on heavier targets like 4 He are straightforward extensions of this study, since the same interaction kernels are used. And the generality of the formalism means that our 3 He densities can be used to evaluate any 3 He elastic-scattering observable with contributions from one- and two-body operators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A generalized and adaptable tensor-contraction-based cluster expansion formalism for multicomponent solids

Density functional theory (DFT)-based simulations of materials have first-principles accuracy, but are very computationally expensive. For simulating various properties of multi-component alloys, the cluster expansion (CE) technique has served as the standard workaround to improve computational efficiency. However, the standard CE technique is difficult to extend to exotic and/or low-symmetry lattices, often implemented via iteration over particular cluster types, which must be enumerated per lattice structure. In this work, we introduce the tensor cluster expansion (TCE), implemented in the open-source code tce-lib, which maps correlation functions to mixed tensor contractions, eliminating the need to iterate over cluster types and additionally making the calculation of correlation functions well-suited for massively parallel architectures like GPUs. We show that local interaction energies are an immediate consequence of the TCE formalism, yielding nearly $\mathcal{O}$(1) energy difference calculations. We then use this formalism to fit CE models for the TaW and CoNiCrFeMn systems, and use these models to respectively compute the enthalpy of mixing curve and Cowley short-range order parameters, showing excellent agreement with ground truth data.

Cluster expansion↗
DOE OSTI2025

Synthesis, Structure, and Redox Reactivity of Ni Complexes Bearing a Redox and Acid–Base Non-innocent Ligand with Ni II , Ni III , and Ni IV Formal Oxidation States

Here, a series of Ni complexes bearing a redox and acid–base noninnocent tetraamido macrocyclic ligand, H 4 -(TAML-4) {H 4 -(TAML-4) = 15,15-dimethyl-5,8,13,17-tetrahydro-5,8,13,17-tetraaza-dibenzo[a,g]cyclotridecene-6,7,14,16-tetraone}, with formal oxidation states of Ni II , Ni III , and Ni IV were synthesized and characterized structurally and spectroscopically. The X-ray crystallographic analysis of the Ni complexes revealed a square planar geometry, and the [Ni(TAML-4)] complex with the formal oxidation state of Ni IV was characterized to be [Ni III (TAML-4 •+ )] with the oxidation state of the Ni III ion and the one-electron oxidized TAML-4 ligand, TAML-4 •+ . The Ni III oxidation state and the TAML-4 radical cation ligand, TAML-4 •+ , were supported by X-ray absorption spectroscopy and density functional theory calculations. The reversible interconversions between [Ni II (TAML-4)] 2– and [Ni III (TAML-4)] − and between [Ni III (TAML-4)] − and [Ni III (TAML-4 •+ )] were demonstrated in spectroelectrochemical measurements as well as in chemical oxidation and reduction reactions. The reactivities of [Ni III (TAML-4)] − and [Ni III (TAML-4 •+ )] were then investigated in hydride transfer reactions using NADH analogs. Hydride transfer from 9,10-dihydro-10-methylacridine (AcrH 2 ) to [Ni III (TAML-4 •+ )] was found to proceed via electron transfer (ET) from AcrH 2 to [Ni III (TAML-4 •+ )] with no deuterium kinetic isotope effect (k H /k D = 1.0(2)). In contrast, hydride transfer from AcrH 2 to [NiIII(TAML-4)] − proceeded much more slowly via a concerted proton-coupled electron transfer (PCET) process with k H /k D = 7.0(5). In the latter reaction, an electron and a proton were transferred to the Ni III center and the TAML-4 ligand, respectively. The mechanisms of the ET by [Ni III (TAML-4 •+ )] and the concerted PCET by [Ni III (TAML-4)] − were ascribed to the different redox potentials of the Ni complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

A formal Fe III/V redox couple in an intercalation electrode

Iron redox cycling between low-valent oxidation states of Fe II and Fe III drives crucial processes in nature. The Fe II/III redox couple charge compensates the cycling of lithium iron phosphate, a positive electrode (cathode) for lithium-ion batteries. High-valent iron redox couples, involving formal oxidation higher than Fe III , could deliver higher electrochemical potentials and energy densities. However, because of the instability of high-valent Fe electrodes, they have proven difficult to probe and exploit in intercalation systems. Here, in this study, we report and characterize a formal Fe III/V redox couple by revisiting the charge compensation mechanism of (de)lithiation in Li 4 FeSbO 6 . Valence-sensitive experimental and computational core-level spectroscopy reveal a direct transition from Fe III (3d 5 ) to a negative-charge-transfer FeV (3d 5 L 2 ) ground state on delithiation, without forming Fe IV , or oxygen dimers. We identify that the cation ordering in Li 4 FeSbO 6 drives a templated phase transition to stabilize the unique Fe V species and demonstrate that disrupting cation ordering suppresses the Fe III/V redox couple. Exhibiting resistance to calendar aging, high operating potential and low voltage hysteresis, the Fe III/V redox couple in Li 4 FeSbO 6 provides a framework for developing sustainable, Fe-based intercalation cathodes for high-voltage applications.

Ramachandran, Hari [Stanford Univ., CA (United Sta↗
DOE OSTI2023

Aromatic and aliphatic hydrocarbon hydroxylation via a formally Ni IV =O oxidant

The reaction of (NMe 4 ) 2 [Ni II (L Ph )(OAc)] (1[OAc], L Ph = 2,2',2''-nitrilo-tris-(N-phenylacetamide); OAc = acetate) with 3-chloroperoxybenzoic acid (m-CPBA) resulted in the formation of a self-hydroxylated Ni III -phenolate complex, 2, where one of the phenyl groups of L Ph underwent hydroxylation. 2 was characterised by UV-Vis, EPR, and XAS spectroscopies and ESI-MS. 2 decayed to yield a previously characterised Ni II -phenolate complex, 3. We postulate that self-hydroxylation was mediated by a formally Ni IV =O oxidant, formed from the reaction of 1[OAc] with m-CPBA, which undergoes electrophilic aromatic substitution to yield 2. This is supported by an analysis of the kinetic and thermodynamic properties of the reaction of 1[OAc] with m-CPBA. Addition of exogenous hydrocarbon substrates intercepted the self-hydroxylation process, producing hydroxylated products, providing further support for the formally Ni IV =O entity. This study demonstrates that the reaction between Ni II salts and m-CPBA can lead to potent metal-based oxidants, in contrast to recent studies demonstrating carboxyl radical is a radical free-chain reaction initiator in Ni II /m-CPBA hydrocarbon oxidation catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Relativistic self-consistent G W : Exact two-component formalism with one-electron approximation for solids

We present a formulation of relativistic self-consistent GW for solids based on the exact two-component formalism with one-electron approximation (X2C1e) and nonrelativistic Coulomb interactions. Our theory allows us to study scalar relativistic effects, spin-orbit coupling, and the interplay of relativistic effects with electron correlation without adjustable parameters. Our all-electron implementation is fully ab initio and does not require a pseudopotential constructed from atomic calculations. We examine the effect of the X2C1e approximation by comparison to the established four-component formalism and reach an excellent agreement. The simplicity of X2C1e enables the construction of higher order theories, such as embedding theories, on top of perturbative calculations.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Self-consistency in GWΓ formalism leading to quasiparticle-quasiparticle couplings

Within many-body perturbation theory, Hedin's formalism offers a systematic way to iteratively compute the self-energy Σ of any dynamically correlated interacting system, provided one can evaluate the interaction vertex Γ exactly. This is, however, impossible, in general, for it involves the functional derivative of Σ with respect to the Green's function. Here, we analyze the structure of this derivative, splitting it into four contributions and outlining the type of quasiparticle interactions that each of them generate. Moreover, we show how, in the implementation of self-consistency, the action of these contributions can be classified into two: A quantitative renormalization of previously included interaction terms and the inclusion of qualitatively distinct interaction terms through successive functional derivatives of Γ itself. Implementing this latter type of self-consistency can extend the validity of perturbative approximations based on Hedin's equations toward the high interaction limit, as we show in the example of the Hubbard dimer. Furthermore, our analysis also provides a unifying perspective on the perturbation theory landscape, showing how the T-matrix approach is completely contained in Hedin's formalism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Neutrinoless double-β decay: Combining quantum Monte Carlo and the nuclear shell model with the generalized contact formalism

Neutrinoless double beta decay searches can determine the Majorana nature of neutrinos, the absolute neutrino mass, and provide invaluable insights on the matter dominance of the universe. However, the uncertainty in the nuclear matrix elements that govern the decay limits the physics reach of these experiments. Here, we devise a novel framework based on the generalized contact formalism that combines the nuclear shell model and quantum Monte Carlo methods and compute the neutrinoless double-beta decay of nuclei used in the most advanced experiments, including 76 Ge, 130 Te, and 136 Xe. Our results cover all relevant terms, including the leading-order short-range operator recognized recently. We validate our method in light nuclei by comparing against accurate variational Monte Carlo results. On heavy systems we obtain reduced nuclear matrix elements compared with previous calculations due to additional correlations captured by quantum Monte Carlo and introduced within the generalized contact formalism, suggesting longer decay half-lives than previously considered. On the other hand, we find an enhancement of the nuclear matrix elements due to the new short-range operator.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Green's function knockout formalism

Knockout nuclear reactions, in which a nucleon is removed from a nucleus as a result of the collision with another nucleus, have been widely used as an experimental tool, both to populate isotopes further removed from stability and to obtain information about the single-particle nature of the nuclear spectrum. In order to fully exploit the experimental information, theory is needed for the description of both the structure of the nuclei involved, and the dynamics associated with the nucleon removal mechanisms. Here, the standard approach, using theoretical shell-model spectroscopic factors for the structure description coupled with an eikonal model of reaction, has been successful when used in the context of the removal of valence nucleons in nuclei close to stability. However, it has been argued that the reaction theory might need to be revisited in the case of exotic nuclei, more specifically for highly asymmetric nuclei in which the deficient species (neutrons or protons) is being removed. We present here a new formalism for the nucleon-removal and -addition reaction through knockout and transfer reactions, that treats consistently structure and reaction properties using dispersive optical potentials. In particular, our formalism includes the dynamical effects associated with the removal of a nucleon from the projectile, which might explain the long standing puzzle of the quenching of spectroscopic factors in nuclei with extreme neutrons-to-protons ratios.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Pseudo-neutrino versus recoil formalism for 4-body phase space and applications to nuclear decay

It is well known that the traditional treatment of radiative corrections that utilizes the “true” neutrino momentum$\overrightarrow{p}_v$ in the differential decay rate formula could lead to a ~α/π systematic error in certain observables due to the mistreatment of 4-body kinematics. Here, I investigate the theory structure of one of the proposed solutions, the “v'-formalism”, in the nonrecoil limit appropriate for neutron and nuclear β decays. I derive an elegant master formula for the 4-body phase space and use it to reanalyze the spectrum-dependent “outer” radiative corrections to the β decay of a polarized spin-half nucleus; a complete set of analytic expressions is provided for readers to straightforwardly obtain the final numerical results. Furthermore, I compare it to the “recoil formalism” where the energy of the recoil nucleus is fixed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Generalized Kompaneets formalism for inelastic neutrino-nucleon scattering in supernova simulations

Based on the Kompaneets approximation, we develop a robust methodology to calculate spectral redistribution via inelastic neutrino-nucleon scattering in the context of core-collapse supernova simulations. The resulting equations conserve lepton number to machine precision and scale linearly, not quadratically, with number of energy groups. The formalism also provides an elegant means to derive the rate of energy transfer to matter which, as it must, automatically goes to zero when the neutrino radiation field is in thermal equilibrium. Furthermore, we derive the next higher order in $ϵ/mc^2$ correction to the neutrino Kompaneets equation. Unlike other Kompaneets schema, ours also generalizes to the case of anisotropic angular distributions, while retaining the conservative form that is a hallmark of the classical Kompaneets equation. In this work, our formalism enables immediate incorporation into supernova codes that follow the spectral angular moments of the neutrino radiation fields.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Gravitational waveforms: A tale of two formalisms

We revisit the quantum-amplitude-based derivation of the gravitational waveform emitted by the scattering of two spinless massive bodies at the third order in Newton’s constant, ℎ ∼ 𝐺 + 𝐺 2 + 𝐺 3 (one-loop level), and correspondingly update its comparison with its classically derived multipolar-post-Minkowskian counterpart. A spurious-pole-free reorganization of the one-loop five-point amplitude substantially simplifies the post-Newtonian expansion. We find complete agreement between the two results up to the fifth order in the small velocity expansion after taking into account three subtle aspects of the amplitude derivation: (1) in agreement with [A. Georgoudis et al., J. High Energy Phys. 03 (2024) 089], the term quadratic in the amplitude in the observable-based formalism [D. A. Kosower et al., J. High Energy Phys. 02 (2019) 137] generates a frame rotation by half the classical scattering angle; (2) the dimensional regularization of the infrared divergences of the amplitude introduces an additional (𝑑 − 4)/(𝑑 − 4) finite term; and (3) zero-frequency gravitons are found to contribute additional terms both at order ℎ ∼ 𝐺 1 and at order ℎ ∼ 𝐺 3 when including disconnected diagrams in the observable-based formalism.

Astronomy & Astrophysics↗
DOE OSTI2024

Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism

We show that the algebra of Parisi ultrametric matrices is recovered by the real-time, replica-free, Dyson-Keldysh equations of infinite-range quantum spin glasses in the late time glassy limit. This connects to earlier results on classical and quantum systems showing how ultrametricity emerges from the persistent slow aging dynamics of the glass phase. The stationary spin glass state thereby spontaneously breaks thermal symmetry, or the Kubo-Martin-Schwinger relation of a state in global thermal equilibrium. We describe the Keldysh path integral of the infinite-range Ising model in transverse and longitudinal fields, and in the context of the Landau expansion of the action functional, show how the long-time limit connects to the full replica symmetry breaking obtained in the equilibrium formalism. We also illustrate our formalism by applying it to the spherical quantum p p -spin model, which only exhibits one-step replica symmetry breaking.

Lang, Johannes (ORCID:0000000283533392)↗
DOE OSTI2020

Calculation Of The First Moment Of Energy Using D-T Reactivity Formalisms Under The Maxwell-Boltzmann Distribution--Part II

Nuclear fusion science is an example of a scientific field with a rich history of expert involvement and scientific publications, which together, form an expert-knowledge base. One example of a nuclear fusion formalism is the utilization of published reaction rates from a variety of authors. Investigators for Deuterium- Tritium (D-T) ion fusion can choose from using frequently cited methods: the Bosch and Hal reactivity, thermonuclear reaction rates from Caughlan and Fowler, and the reactivity evaluation from Miley, Towner & Ivich which forms the basis of the Naval Research Lab (NRL) formulary. There are other choices available. Each of the reactivity formulations considered here, are based upon the Maxwell-Boltzmann velocity distribution for D-T fusion ion reactants. Numerical methods for computer codes simulating hot, energetic plasmas, include tabulations of the reactivity, and the first moment of energy. This report continues the step toward building understanding of nuclear fusion reactivity formalisms. It is part of a series of reports with the same goal, [5-10] and is the continuation of the Part I paper for defining the mathematical relationship of the first moment of D-T fusion ion kinetic energy, <$E$>, with the fusion cross-section, fusion reactivity and its derivative with ion-temperature. In Part I, three variants of the first moment <$E$> were analytically developed and explored: 1) constant cross-section, 2) a normalized first moment, and 3) a particular function of the first moment from Brysk. In Part II, attention is given to the definition of <$K$>, originally described as a ratio of moments from Brysk, and its relationship to the first moment definitions from Part I. One measure of the progress made in these documents is the identification that Brysk’s ratio of the second moment to the first moment ratio, <$K$>, does not correspond to his provided solution of the first moment of energy. Another measure of (our) progress from this work is the comparison of first moment variants. That comparison includes confirming the importance of cross sections defined in terms of energy. The analytical relationships we have developed among important physics quantities are useful tools in validation and verification (V&V). For example, we can calculate the kinetic energy as a mean or as a first moment, or as a function of the first moment. These analytically-determined values can be compared directly with numerically-determined values, supplied to the authors, representing <$E$>.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗