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DOE OSTI2025

Characterizing IHE Response to Multiple Shock Loading

The response of high explosives to shock loading is traditionally measured with a steady loading pressure. In many accident scenarios involving fragment impact, however, a loading duration that is shorter than the build up to detonation may occur. Fragments passing through multiple materials before reaching a high explosive charge may produce loading that is comprised of more than one shock wave. Additionally, the build up to detonation in high explosive corner turning loads the explosive a short duration pressure pulse, since rarefactions can often rapidly overtake the reactive wave. For these reasons, we have studied the response of the insensitive high explosive (IHE) materials PBX 9502 and LX-17 to complex loadings of varied intensity and duration. We refer to a single loading of limited duration as a “thin pulse”, whereas more complex scenarios were studied with an impactor that produces a double shock in the explosive. The following report presents experimental data and analyses of thin pulse shock initiation and double shock experiments designed to guide development of models of Insensitive High Explosives (IHEs) under controlled one-dimensional conditions relevant to accident scenarios and corner turning. Thin pulse shock initiation data on PBX 9502 and LX-17 were obtained under varied pulse duration, pressed density, and temperature conditions in order to probe various parameters essential for the development of a physics-based Cheetah reactive flow hotspot model. In situ pressure gauges provide insight into the degree of reaction in the explosive that are not obtainable with optical PDV measurements or distance measurements such as run to detonation. Double shock data was obtained to inform a Composition Aware Cheetah model which can be applied to any TATB-based IHEs. This model supports efforts to find a new IHE formulation and potentially incorporate new binders into IHE formulations. Simulations of each experiment are included to demonstrate the utility of these focused experiments to developing models of HE behavior. One-dimensional gas gun experiments are essential for characterizing shocked HE behavior and informing HE models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Covariant color-kinematics duality

We show that color-kinematics duality is a manifest property of the equations of motion governing currents and field strengths. For the nonlinear sigma model (NLSM), this insight enables an implementation of the double copy at the level of fields, as well as an explicit construction of the kinematic algebra and associated kinematic current. As a byproduct, we also derive new formulations of the special Galileon (SG) and Born-Infeld (BI) theory. For Yang-Mills (YM) theory, this same approach reveals a novel structure — covariant color-kinematics duality — whose only difference from the conventional duality is that 1/$\square$ is replaced with covariant 1/D 2 . Remarkably, this structure implies that YM theory is itself the covariant double copy of gauged biadjoint scalar (GBAS) theory and an F 3 theory of field strengths encoding a corresponding kinematic algebra and current. Directly applying the double copy to equations of motion, we derive general relativity (GR) from the product of Einstein-YM and F 3 theory. This exercise reveals a trivial variant of the classical double copy that recasts any solution of GR as a solution of YM theory in a curved background. Covariant color-kinematics duality also implies a new decomposition of tree-level amplitudes in YM theory into those of GBAS theory. Using this representation we derive a closed-form, analytic expression for all BCJ numerators in YM theory and the NLSM for any number of particles in any spacetime dimension. By virtue of the double copy, this constitutes an explicit formula for all tree-level scattering amplitudes in YM, GR, NLSM, SG, and BI.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Euclidean correlation functions in quantum gravity

We calculate Euclidean correlation functions through next-to-leading order in the low-energy effective theory of gravity. We focus on correlation functions of curvature and volume operators, calculating these functions through one-loop order. We show that quantum fluctuations of the background spacetime must be taken into account in order to obtain gauge invariant expressions, and we point out a subtlety associated with the analytic continuation of the conformal mode. Our final expressions for the correlation functions involve only Newton’s constant and the source-sink separation, and they are a universal prediction of the low-energy effective theory. Thus, they serve as a useful point of comparison for nonperturbative lattice formulations of gravity.

Effective field theory↗

DOE OSTI2021

Trimeron-phonon coupling in magnetite

Using density functional theory, we study the lattice dynamical properties of magnetite (Fe 3 O 4 ) in the high-temperature cubic and low-temperature monoclinic phases. The calculated phonon dispersion curves and density of states are compared with the available experimental data obtained by inelastic neutron, inelastic x-ray, and nuclear inelastic scattering. We find a very good agreement between the theoretical and experimental results for the monoclinic Cc structure revealing the strong coupling between the charge-orbital (trimeron) order and specific phonon modes. For the cubic phase, clear discrepancies arise due to fluctuation effects, which are not included in the calculation method. Despite this shortcoming, we argue that the main spectral features can be understood assuming that the strong trimeron-phonon coupling is extended above the Verwey transition, with lattice dynamics influenced by the short-range order instead of the average cubic structure. Our results indicate the validity of trimerons (and trimeron-phonon coupling) to explain the physics of magnetite much beyond their original formulation.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Real-space chirality from crystalline topological defects in the Kitaev spin liquid

We show that certain crystalline topological defects in the gapless Kitaev honeycomb spin liquid model generate a chirality and Majorana fermion orbital magnetization that depends in a universal manner on their emergent flux. Focusing on 5–7 dislocations as building blocks, consisting of pentagon and heptagon disclinations, we identify the Kitaev bond label configurations that preserve solvability. By computing two formulations of local markers M(r) we find that the 5 and 7 lattice defects generate a real-space contribution to Chern number and an associated Majorana fermion orbital magnetization proportional to M(r). The sign of the M(r) contribution from each 5/7 defect, i.e. its q M = ± 1 chirality, is determined by the defect Frank angle sign F and emergent gauge field flux W = ± i through the expression q M = − iFW. Remarkably, though lattice curvature and torsion can interplay with the surrounding gapless background to modify the profile of M(r), its sign q M is determined locally, implying that crystalline defects in the Kitaev spin liquid can generate a robust and observable chirality.

Magnetic properties and materials↗

DOE OSTI2022

A novel formulation of the unintegrated gluon distribution for DIS

We provide a semi-classical description of the inclusive gluon mediated Deep Inelastic Scattering cross section in a way that accounts for the leading powers in both the Regge and Bjorken limits. Our approach thus allows a systematic matching of small and moderate xBj regimes of gluon proton structure functions. We find a new unintegrated gluon distribution with an explicit dependence on the longitudinal momentum fraction x which entirely spans both the dipole operator and the gluonic Parton Distribution Function. Computing this gauge invariant gluon operator on the lattice could allow to probe the energy dependence of the saturation scale from first principles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Conservation of Dry Air, Water, and Energy in CAM and Its Potential Impact on Tropical Rainfall

Abstract For the Community Atmosphere Model version 6 (CAM6), an adjustment is needed to conserve dry air mass. This adjustment exposes an inconsistency in how CAM6’s energy budget incorporates water—in CAM6 water in the vapor phase has energy, but condensed phases of water do not. When water vapor condenses, only its latent energy is retained in the model, while its remaining internal, potential, and kinetic energy are lost. A global fixer is used in the default CAM6 model to maintain global energy conservation, but locally the energy tendency associated with water changing phase violates the divergence theorem. This error in energy tendency is intrinsically tied to the water vapor tendency, and reaches its highest values in regions of heavy rainfall, where the error can be as high as 40 W m −2 annually averaged. Several possible changes are outlined within this manuscript that would allow CAM6 to satisfy the divergence theorem locally. These fall into one of two categories: 1) modifying the surface flux to balance the local atmospheric energy tendency and 2) modifying the local atmospheric tendency to balance the surface plus top-of-atmosphere energy fluxes. To gauge which aspects of the simulated climate are most sensitive to this error, the simplest possible change—where condensed water still does not carry energy and a local energy fixer is used in place of the global one—is implemented within CAM6. Comparing this experiment with the default configuration of CAM6 reveals precipitation, particularly its variability, to be highly sensitive to the energy budget formulation. Significance Statement This study examines and explains spurious regional sources and sinks of energy in a widely used climate model. These energy errors result from not tracking energy associated with water after it transitions from the vapor phase to either liquid or ice. Instead, the model used a global fixer to offset the energy tendency related to the energy sources and sinks associated with condensed water species. We replace this global fixer with a local one to examine the model sensitivity to the regional energy error and find a large sensitivity in the simulated hydrologic cycle. This work suggests that the underlying thermodynamic assumptions in the model should be revisited to build confidence in the model-simulated regional-scale water and energy cycles.

Harrop, Bryce E.↗

DOE OSTI2023

Scalar Breit interaction for molecular calculations

Variational treatment of the Dirac–Coulomb–Gaunt or Dirac–Coulomb–Breit two-electron interaction at the Dirac–Hartree–Fock level is the starting point of high-accuracy four-component calculations of atomic and molecular systems. In this work, we introduce, for the first time, the scalar Hamiltonians derived from the Dirac–Coulomb–Gaunt and Dirac–Coulomb–Breit operators based on spin separation in the Pauli quaternion basis. While the widely used spin-free Dirac–Coulomb Hamiltonian includes only the direct Coulomb and exchange terms that resemble nonrelativistic two-electron interactions, the scalar Gaunt operator adds a scalar spin–spin term. The spin separation of the gauge operator gives rise to an additional scalar orbit-orbit interaction in the scalar Breit Hamiltonian. Benchmark calculations of Au n (n = 2–8) show that the scalar Dirac–Coulomb–Breit Hamiltonian can capture 99.99% of the total energy with only 10% of the computational cost when real-valued arithmetic is used, compared to the full Dirac–Coulomb–Breit Hamiltonian. In conclusion, the scalar relativistic formulation developed in this work lays the theoretical foundation for the development of high-accuracy, low-cost correlated variational relativistic many-body theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Quarkonium suppression in strongly coupled plasmas

Suppression of open heavy quarks and quarkonia in heavy-ion collisions are among the most informative probes of quark-gluon plasma (QGP). Interpreting the full wealth of data obtained from the collision events requires a precise theoretical understanding of the evolution of heavy quarks and quarkonia as they propagate through a strongly coupled plasma. Such calculations require the evaluation of a gauge-invariant correlator of chromoelectric fields. This chromoelectric correlator encodes all the characteristics of QGP that the dissociation and recombination dynamics of quarkonium are sensitive to, which is to say can in principle measure. We review its distinctive qualitative features at weak coupling in QCD up to next-to-leading order and at strong coupling in N = 4 SYM using the AdS/CFT correspondence, as well as its formulation in Euclidean QCD. Furthermore, we report on recent progress in applying our results to the calculation of the final quarkonium abundances after propagating through a cooling droplet of QGP, which illustrates how we may learn about QGP from quarkonium measurements. We devote special attention to how the presence of a strongly coupled plasma modifies the transport description of quarkonium, in comparison to approaches that rely on weak coupling approximations to describe quarkonium dissociation and recombination.

Scheihing-Hitschfeld, Bruno [University of Califor↗

NASA NTRS1989

A hybrid-perturbation-Galerkin technique which combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗

NASA NTRS1990

A hybrid perturbation-Galerkin technique that combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be used to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗

NASA NTRS1996

Coupled Structural, Thermal, Phase-change and Electromagnetic Analysis for Superconductors, Volume 2

Described are the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromag subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements, (2) finite element modeling of the electromagnetic problem, (3) coupling of thermel and mechanical effects, and (4) computer implementation and solution of the superconductivity transition problem. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles, (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements, and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects, and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The theoretical development is described in two volumes. Volume 1 describes mostly formulation specific problems. Volume 2 describes generalization of those formulations.

Felippa, C. A.↗

NASA NTRS2011

Dynamic Shape Reconstruction of Three-Dimensional Frame Structures Using the Inverse Finite Element Method

A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.

Gherlone, Marco↗

NASA NTRS1996

Coupled Structural, Thermal, Phase-Change and Electromagnetic Analysis for Superconductors

Described are the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromagnetic subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase-change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements, (2) finite element modeling of the electromagnetic problem, (3) coupling of thermal and mechanical effects, and (4) computer implementation and solution of the superconductivity transition problem. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles, (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements, and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects, and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The theoretical development is described in two volumes. This volume, Volume 1, describes mostly formulations for specific problems. Volume 2 describes generalization of those formulations.

Felippa, C. A.↗

DOE OSTI2026

Perturbative second-order optical susceptibility of bulk materials: a symmetry-enforced return to non-orthogonal localized basis sets

The second-order optical susceptibility of semiconductors $\chi^{(2)}_{ijk}(-2\omega;\omega,\omega)$ finds application in metrology, spectroscopy, telecommunications, material characterization, and quantum information. Pioneering calculations of $\chi^{(2)}_{ijk}(-2\omega;\omega,\omega)$ utilized non-orthogonal Gaussian orbitals centered at atoms. That formulation transitioned into plane-wave-based algorithms as time went by. As of late, nevertheless, multiple tools for calculating optical susceptibilities have recast the problem using Wannier (i.e. localized) orbitals, making a comeback onto frameworks based on localized basis sets. Here, in this work, we present an approach for calculating $\chi^{(2)}_{ijk}(-2\omega;\omega,\omega)$ reliant on numerical pseudo-atomic orbitals (PAOs) within perturbation theory in the velocity gauge. Its salient feature is a calculation of ‘Slater–Koster-like’ two-center integrals of the momentum operator in between PAOs identified by symmetry. The approach was successfully tested on paradigmatic cubic silicon carbide (3C-SiC) and gallium arsenide, for which linear responses are contributed as well.

Huamán, Angiolo [Univ. of Arkansas, Fayetteville, ↗

NASA NTRS1990

Theoretical and numerical difficulties in 3-D vector potential methods in finite element magnetostatic computations

This paper describes the results of application of three well known 3D magnetic vector potential (MVP) based finite element formulations for computation of magnetostatic fields in electrical devices. The three methods were identically applied to three practical examples, the first of which contains only one medium (free space), while the second and third examples contained a mix of free space and iron. The first of these methods is based on the unconstrained curl-curl of the MVP, while the second and third methods are predicated upon constraining the divergence of the MVP 10 zero (Coulomb's Gauge). It was found that the two latter methods cease to give useful and meaningful results when the global solution region contains a mix of media of high and low permeabilities. Furthermore, it was found that their results do not achieve the intended zero constraint on the divergence of the MVP.

Demerdash, N. A.↗

DOE OSTI2020

From Navier-Stokes to Maxwell via Einstein

We revisit the cutoff surface formulation of fluid-gravity duality in the context of the classical double copy. The spacetimes in this fluid-gravity duality are algebraically special, with Petrov type II when the spacetime is four dimensional. We find two special classes of fluids whose dual spacetimes exhibit higher algebraic speciality: constant vorticity flows have type D gravity duals, while potential flows map to type N spacetimes. Using the Weyl version of the classical double copy, we construct associated single-copy gauge fields for both cases, finding that constant vorticity fluids map to a solenoid gauge field. Additionally we find the scalar in a potential flow fluid maps to the zeroth copy scalar.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2017

Improvements to Wire Bundle Thermal Modeling for Ampacity Determination

Determining current carrying capacity (ampacity) of wire bundles in aerospace vehicles is critical not only to safety but also to efficient design. Published standards provide guidance on determining wire bundle ampacity but offer little flexibility for configurations where wire bundles of mixed gauges and currents are employed with varying external insulation jacket surface properties. Thermal modeling has been employed in an attempt to develop techniques to assist in ampacity determination for these complex configurations. Previous developments allowed analysis of wire bundle configurations but was constrained to configurations comprised of less than 50 elements. Additionally, for vacuum analyses, configurations with very low emittance external jackets suffered from numerical instability in the solution. A new thermal modeler is presented allowing for larger configurations and is not constrained for low bundle infrared emissivity calculations. Formulation of key internal radiation and interface conductance parameters is discussed including the effects of temperature and air pressure on wire to wire thermal conductance. Test cases comparing model-predicted ampacity and that calculated from standards documents are presented.

Rickman, Steve L.↗