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All sources NASA NTRS DOE OSTI

DOE OSTI2025

Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: Hilbert space of a trivalent vertex

The construction of gauge-invariant states of SU(3) lattice gauge theories has garnered new interest in recent years, but implementing them is complicated by the need for SU(3) Clebsch-Gordon coefficients. In the loop-string-hadron (LSH) approach to lattice gauge theories, the elementary excitations are strictly gauge invariant, and constructing the basis requires no knowledge of Clebsch-Gordon coefficients. Originally developed for SU(2), the LSH formulation was recently generalized to SU(3), but limited to one spatial dimension. In this work, we generalize the LSH approach to constructing the basis of SU(3) gauge-invariant states at a trivalent vertex—the essential building block to multidimensional space. A direct generalization from the SU(2) vertex yields a legitimate basis; however, in certain sectors of the Hilbert space, the naive LSH basis vectors so defined suffer from being nonorthogonal. The issues with orthogonality are directly related to the “missing label” or “outer multiplicity” problem associated with SU(3) tensor products and may also be phrased in terms of Littlewood-Richardson coefficients or the need for a “seventh Casimir” operator. The states that are unaffected by the problem are orthonormalized in closed form. For the sectors that are afflicted, we discuss the nonorthogonal bases and their orthogonalization. A few candidates for seventh Casimir operators are readily constructed from the suite of LSH gauge-singlet operators. The diagonalization of a seventh Casimir represents one prescriptive solution toward obtaining a complete orthonormal basis, but a closed-form general solution remains to be found. Published by the American Physical Society 2025

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1988

Conditions for the validity of unmagnetized-plasma theory in describing weakly magnetized plasmas

The application of the unmagnetized-plasma theory to the derivation of the expression for the dielectric tensor for weakly magnetized plasmas is examined. The analysis of Baldwin et. al. (1969) is employed to determine the conditions under which the magnetic effects on the dielectric tensor of a plasma are small. The relation between wave and plasma parameters and the plasma distribution function is studied. Axisymmetric distribution functions in magnetized plasma are considered. The derived conditions are analyzed in terms of resonance ellipses of the cyclotron maser theory. Examples are presented in which the conditions are applied to a nonrelativistic Maxwellian distribution and the dispersion and instability of Langmuir and Bernstein waves in weakly magnetized plasma. The data reveal that the conditions under which the magnetic field can be completely neglected depend on the forms of the distribution function.

Robinson, P. A.↗

DOE OSTI2021

Large rotations of the grain-scale stress tensor during yielding set the stage for failure

The stress-state within individual grains in a polycrystal determine the fate of the aggregate including mechanical failure. By tracking the evolution of the stress tensor throughout the elastoplastic transition, large rotations of the stress-state, which have long been theorized to occur, are observed experimentally for the first time. These stress rotations (~15°) are more than an order of magnitude larger than the concomitant crystallographic lattice reorientations (~0.9°) well-known to occur during metal plasticity. Furthermore, these rotations are accompanied by a decrease in stress triaxiality within certain grains, promote strain softening, and set the stage for failure at an early stage of deformation. Finally, these results provide a completely new perspective through which to contemplate the question of “hot-spots” responsible for failure of high-performance structural materials.

36 MATERIALS SCIENCE↗

NASA NTRS1993

The nonlinear Galerkin method: A multi-scale method applied to the simulation of homogeneous turbulent flows

Using results of Direct Numerical Simulation (DNS) in the case of two-dimensional homogeneous isotropic flows, the behavior of the small and large scales of Kolmogorov like flows at moderate Reynolds numbers are first analyzed in detail. Several estimates on the time variations of the small eddies and the nonlinear interaction terms were derived; those terms play the role of the Reynolds stress tensor in the case of LES. Since the time step of a numerical scheme is determined as a function of the energy-containing eddies of the flow, the variations of the small scales and of the nonlinear interaction terms over one iteration can become negligible by comparison with the accuracy of the computation. Based on this remark, a multilevel scheme which treats differently the small and the large eddies was proposed. Using mathematical developments, estimates of all the parameters involved in the algorithm, which then becomes a completely self-adaptive procedure were derived. Finally, realistic simulations of (Kolmorov like) flows over several eddy-turnover times were performed. The results are analyzed in detail and a parametric study of the nonlinear Galerkin method is performed.

Debussche, A.↗

DOE OSTI2021

Reduced scaling formulation of CASPT2 analytical gradients using the supporting subspace method

We present a reduced scaling and exact reformulation of state specific complete active space second-order perturbation (CASPT2) analytical gradients in terms of the MP2 and Fock derivatives using the supporting subspace method. This work follows naturally from the supporting subspace formulation of the CASPT2 energy in terms of the MP2 energy using dressed orbitals and Fock builds. For a given active space configuration, the terms corresponding to the MP2-gradient can be evaluated with O(N5) operations, while the rest of the calculations can be computed with O(N3) operations using Fock builds, Fock gradients, and linear algebra. When tensor-hyper-contraction is applied simultaneously, the computational cost can be further reduced to O(N4) for a fixed active space size. The new formulation enables efficient implementation of CASPT2 analytical gradients by leveraging the existing graphical processing unit (GPU)-based MP2 and Fock routines. We present benchmark results that demonstrate the accuracy and performance of the new method. Example applications of the new method in ab initio molecular dynamics simulation and constrained geometry optimization are given.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

CFTs blueshift tensor fluctuations universally

The strong constraints of conformal symmetry cause any nearly-conformal sector to blueshift tensor fluctuations in cosmology. Hidden sectors with approximate conformal symmetry, which may be quite large, are a well-motivated extension of physics beyond the Standard Models of particle physics and cosmology. They can therefore lead to a detectable shift in the tensor tilt for next-generation CMB and gravitational wave experiments. Here, we compute the leading-order contribution to the in-in graviton two-point function from virtual loops in such sectors to demonstrate this universal effect. In units where a single conformally-coupled scalar is 1, limits from Stage-IV CMB experiments could bound the size of this extra sector to be smaller than ~10 15 , under a plausible calculational assumption backed by a simple power counting argument. This would be sufficient to rule out N-Naturalness as a complete resolution of the hierarchy problem.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Exact matrix product state representation and convergence of a fully correlated electronic wavefunction in the infinite-basis limit

Here In this paper we present the exact representation of a fully correlated electronic wavefunction as the single-particle basis approaches completeness. It consists of a half-infinite chain of matrices of exponentially increasing size. The complete basis limit is illustrated numerically using the density-matrix renormalization-group method by computing the core-valence entanglement in the C 2 ground state in increasing subsets of cc-pVTZ and pVQZ bases until convergence is reached.

36 MATERIALS SCIENCE↗

NASA NTRS1987

The decay of isotropic turbulence in a rapidly rotating frame

A direct numerical simulation of the decay of initially isotropic turbulence in a rapidly rotating frame was conducted. This 128 x 128 x 128 simulation was completed for a Reynolds number Re sub lambda = 15.3 and a Rossby number Ro sub lambda = 0.07 based on the initial turbulent kinetic energy and Taylor microscale. The numerical results indicate that the turbulence remains essentially isotropic during the major part of the decay (i.e., beyond the point where the turbulent kinetic energy has decayed to less than 10 percent of its initial value). The rapid rotation has the primary effect of shutting off the energy transfer so that the turbulence dissipation (and hence the rate of decay of the turbulent kinetic energy) is substantially reduced. Consequently, the anisotropy tensor remains essentially unchanged while the energy spectrum undergoes a nearly linear viscous decay (the same results that are predicted by Rapid Distortion Theory which is only formally valid for much shorter elapsed times. Surprisingly, no Taylor-Proudman reorganization of the flow to a two-dimensional state is observed. The implications that these results have on turbulence modeling are discussed briefly along with prospective future research.

Speziale, C. G.↗

NASA NTRS1985

Dynamic Creep Buckling: Analysis of Shell Structures Subjected to Time-dependent Mechanical and Thermal Loading

The objective of the present research is to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. A complete, true ab-initio rate theory of kinematics and kinetics for continuum and curved thin structures, without any restriction on the magnitude of the strains or the deformations, was formulated. The time dependence and large strain behavior are incorporated through the introduction of the time rates of metric and curvature in two coordinate systems: fixed (spatial) and convected (material). The relations between the time derivative and the covariant derivative (gradient) were developed for curved space and motion, so the velocity components supply the connection between the equations of motion and the time rates of change of the metric and curvature tensors.

Simitses, G. J.↗

DOE OSTI2025

Frequency-Selectable Laser Source (FLS) for Cosmic Microwave Background Experiments

Cosmic Microwave Background (CMB) experiments measure remnant radiation from the early universe and use that data to determine fundamental properties of the universe. We can constrain key parameters, such as \textit{r}, the cosmic tensor-to-scalar ratio, and $N_\text{eff}$, the effective number of relativistic species, by analyzing the CMB power spectra. Improving our measurements of the CMB requires improving our instrument systematics, one of the most important of which is detector bandpass. Current experiments use a Fourier Transform Spectrometer (FTS) to measure bandpass. However, the FTS is systematics limited, and cannot achieve the accuracy needed to make improved CMB measurements. For this reason, we are developing a new instrument, the Frequency-Selectable Laser Source (FLS) to decrease the uncertainty in bandpass by an order of magnitude. In this paper, we describe work completed to support the version 2 upgrade to the FLS. Using ray-tracing software, we modeled the FLS optics to set physical tolerances for the new design. We also discuss the laser calibration, and future work to be completed in further development of the FLS upgrade.

Rosen-Turits, Gabriel M.↗

NASA NTRS2017

Behavioral, Brain Imaging and Genomic Measures to Predict Functional Outcomes Post-Bed Rest and Space Flight

Astronauts experience sensorimotor disturbances during their initial exposure to microgravity and during the re-adaptation phase following a return to an Earth-gravitational environment. These alterations may disrupt crewmembers' ability to perform mission critical functional tasks requiring ambulation, manual control and gaze stability. Interestingly, astronauts who return from spaceflight show substantial differences in their abilities to readapt to a gravitational environment. The ability to predict the manner and degree to which individual astronauts are affected will improve the effectiveness of countermeasure training programs designed to enhance sensorimotor adaptability. For such an approach to succeed, we must develop predictive measures of sensorimotor adaptability that will allow us to foresee, before actual spaceflight, which crewmembers are likely to experience greater challenges to their adaptive capacities. The goals of this project are to identify and characterize this set of predictive measures. Our approach includes: 1) behavioral tests to assess sensory bias and adaptability quantified using both strategic and plastic-adaptive responses; 2) imaging to determine individual brain morphological and functional features, using structural magnetic resonance imaging (MRI), diffusion tensor imaging, resting state functional connectivity MRI, and sensorimotor adaptation task-related functional brain activation; and 3) assessment of genetic polymorphisms in the catechol-O-methyl transferase, dopamine receptor D2, and brain-derived neurotrophic factor genes and genetic polymorphisms of alpha2-adrenergic receptors that play a role in the neural pathways underlying sensorimotor adaptation. We anticipate that these predictive measures will be significantly correlated with individual differences in sensorimotor adaptability after long-duration spaceflight and exposure to an analog bed rest environment. We will be conducting a retrospective study, leveraging data already collected from relevant ongoing or completed bed rest and spaceflight studies. This data will be combined with predictor metrics that will be collected prospectively (as described for behavioral, brain imaging and genomic measures) from these returning subjects to build models for predicting post spaceflight and bed rest adaptive capability. In this presentation we will discuss the optimized set of tests for predictive metrics to be used for evaluating post mission adaptive capability as manifested in their outcome measures. Comparisons of model performance will allow us to better design and implement sensorimotor adaptability training countermeasures against decrements in post-mission adaptive capability that are customized for each crewmember's sensory biases, adaptive ability, brain structure, brain function, and genetic predispositions. The ability to customize adaptability training will allow more efficient use of crew time during training and will optimize training prescriptions for astronauts to mitigate the deleterious effects of spaceflight.

Mulavara, A. P.↗

DOE OSTI2025

Frequency-Selectable Laser Source for Cosmic Microwave Background Experiments

Rosen-Turits, Gabriel M. [Fermilab]↗

NASA NTRSDate not supplied

Multi-Scale Analysis of Effective Mechanical Properties of 3D Woven Composite Materials

This work aims to compute and analyze the mechanical properties of 3D woven composite materials that share the same yarn structure but differ in their matrix porosity and fiber volume fraction. Assuming linear elastic behavior, the software PuMA, developed at NASA, was used to characterize the different composites from their constituents' data averaging their elastic properties in three main directions to obtain their effective orthotropic mechanical properties. This was performed in three steps: firstly, the different phases (yarns/matrix) were analyzed as anisotropic materials separately at the micro-scale; then, the results from these analyses were homogenized and used to obtain the anisotropic elasticity tensor at the meso-scale for the different woven materials; and finally, assuming orthotropic mechanical behavior for the unit cell the mechanical properties were obtained at the macro-scale. The 3D woven composite materials selected for this study are made of phenolic resin with porosity values between 0 and 0.6, and resin infiltrated carbon fiber with volume fractions between 0.5 and 0.9 for the yarns. Results from PuMA were validated with external FEA simulations for the non-porous 3D woven material with a fiber volume fraction of 0.9 in the yarns. Results will be included in the final paper after completing the study detailed in Section II.

Sergio Fraile Izquierdo↗

NASA NTRS2016

Behavioral, Brain Imaging and Genomic Measures to Predict Functional Outcomes Post - Bed Rest and Spaceflight

Astronauts experience sensorimotor disturbances during their initial exposure to microgravity and during the re-adaptation phase following a return to an Earth-gravitational environment. These alterations may disrupt crewmembers' ability to perform mission critical functional tasks requiring ambulation, manual control and gaze stability. Interestingly, astronauts who return from spaceflight show substantial differences in their abilities to readapt to a gravitational environment. The ability to predict the manner and degree to which individual astronauts would be affected would improve the effectiveness of countermeasure training programs designed to enhance sensorimotor adaptability. For such an approach to succeed, we must develop predictive measures of sensorimotor adaptability that will allow us to foresee, before actual spaceflight, which crewmembers are likely to experience the greatest challenges to their adaptive capacities. The goals of this project are to identify and characterize this set of predictive measures. Our approach includes: 1) behavioral tests to assess sensory bias and adaptability quantified using both strategic and plastic-adaptive responses; 2) imaging to determine individual brain morphological and functional features, using structural magnetic resonance imaging (MRI), diffusion tensor imaging, resting state functional connectivity MRI, and sensorimotor adaptation task-related functional brain activation; and 3) assessment of genotypic markers of genetic polymorphisms in the catechol-O-methyl transferase, dopamine receptor D2, and brain-derived neurotrophic factor genes and genetic polymorphisms of alpha2-adrenergic receptors that play a role in the neural pathways underlying sensorimotor adaptation. We anticipate that these predictive measures will be significantly correlated with individual differences in sensorimotor adaptability after long-duration spaceflight and exposure to an analog bed rest environment. We will be conducting a retrospective study, leveraging data already collected from relevant ongoing or completed bed rest and spaceflight studies. These data will be combined with predictor metrics that will be collected prospectively (as described for behavioral, brain imaging and genomic measures) from these returning subjects to build models for predicting post-mission (bed rest - non-astronauts or space flight - astronauts) adaptive capability as manifested in their outcome measures. To date we have completed a study on 15 normal subjects with all of the above measures. In this presentation we will discuss the optimized set of tests for predictive metrics to be used for evaluating post mission adaptive capability as manifested in their outcome measures. Comparisons of model performance will allow us to better design and implement sensorimotor adaptability training countermeasures against decrements in post-mission adaptive capability that are customized for each crewmember's sensory biases, adaptive capacity, brain structure and functional capacities, and genetic predispositions. The ability to customize adaptability training will allow more efficient use of crew time during training and will optimize training prescriptions for astronauts to ensure expected outcomes.

Mulavara, A. P.↗

NASA NTRS2021

Organized kinetic energy backscatter in the hurricane boundary layer from radar measurements

The fluid mechanics of hurricanes strongly depends on boundary layer energetics due to the warm-core nature of the system with peak velocities located at lower levels. One barrier that has inhibited a more complete characterization of energy transfer in the boundary layer is a lack of observations that resolve large, turbulent eddies. In particular, the occurrence and structure of upscale energy transfer (backscatter) in the hurricane boundary layer as well as the effects of backscatter on the vortex intensity are unknown. The analysis presented here of very high-resolution, three-dimensional wind observations from Hurricane Rita (2005) at peak intensity reveals large regions of organized backscatter in the boundary layer associated with coherent, turbulent eddies. Strong forwardscatter is also found next to the backscatter regions due to the interaction between adjacent eddies. Two components of the stress tensor are primarily responsible for this alternating scatter structure, as shown by large correlation coefficients between the fields: the radial–vertical component (τ13) and the azimuthal–vertical component (τ23) with average correlations of 79% and 49 %, respectively. The Leonard, Reynolds and cross-term stress components are also provided. The impact of the sub-filter-scale energy transfer is estimated by computing the kinetic energy budget for the resolved-scale and eddy-scale motions. The results show that the sub-filter-scale energy transfer term is of the same order as the other terms in the eddy-scale budgets, contributing between 16% and 40% to the local time tendency with an average contribution of approximately 30 %. These results indicate that the coherent turbulent eddies can affect the vortex dynamics through wave–wave nonlinear interactions, which can subsequently influence the wave–mean flow interactions. This is the first study to examine the full sub-filter-scale

Sydney Sroka↗

DOE OSTI2023

Stability of hairy black holes in shift-symmetric scalar-tensor theories via the effective field theory approach

Shift-symmetric Horndeski theories admit an interesting class of Schwarzschild-de Sitter black hole solutions exhibiting time-dependent scalar hair. The properties of these solutions may be studied via a bottom-up effective field theory (EFT) based on the background symmetries. This is in part possible by making use of a convenient coordinate choice — Lemaître-type coordinates — in which the profile of the Horndeski scalar field is linear in the relevant time coordinate. We construct this EFT, and use it to understand the stability of hairy black holes in shift-symmetric Horndeski theories, providing a set of constraints that the otherwise-free functions appearing in the Horndeski Lagrangian must satisfy in order to admit stable black hole solutions. The EFT is analyzed in the decoupling limit to understand potential sources of instability. Further, we also perform a complete analysis of the EFT with odd-parity linear perturbations around general spherically symmetric space-time.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1987

Nonisothermal elasto-visco-plastic response of shell-type structures

A mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads is disussed. Among the system responses, which are associated with these load conditions, are thermal buckling and creep buckling. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and have been considered in the development of the mathematical model. Furthermore, this was accommodated in the solution procedures. A complete true ab-inito rate theory of kinematics and kinetics for continuum and curved thin structures, without any restriction on the magnitude of the strains or the deformation, was formulated. The time dependence and large strain behavior are incorporated through the introduction of the time rates of the metric and curvature in two coordinate systems, a fixed (spatial) one and a convected (material) coordinate system. The relations between the time derivative and the covariant derivatives (gradients) have been developed for curved space and motion, so that the velocity components supply the connection between the equations of motion and the time rate of change of the metric and curvature tensors.

Simitses, G. J.↗

DOE OSTI2021

Next-to-$\mathrm{MHV}$ Yang-Mills kinematic algebra

Kinematic numerators of Yang-Mills scattering amplitudes possess a rich Lie algebraic structure that suggest the existence of a hidden infinite-dimensional kinematic algebra. Explicitly realizing such a kinematic algebra is a longstanding open problem that only has had partial success for simple helicity sectors. In past work, we introduced a framework using tensor currents and fusion rules to generate BCJ numerators of a special subsector of NMHV amplitudes in Yang-Mills theory. Here we enlarge the scope and explicitly realize a kinematic algebra for all NMHV amplitudes. Master numerators are obtained directly from the algebraic rules and through commutators and kinematic Jacobi identities other numerators can be generated. Inspecting the output of the algebra, we conjecture a closed-form expression for the master BCJ numerator up to any multiplicity. We also introduce a new method, based on group algebra of the permutation group, to solve for the generalized gauge freedom of BCJ numerators. It uses the recently introduced binary BCJ relations to provide a complete set of NMHV kinematic numerators that consist of pure gauge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗