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DOE OSTI2022

A New Proof That the Number of Linear Elastic Symmetries in Two Dimensions Is Four

In this work, we present an elementary and self-contained proof that there are exactly four symmetry classes of the elasticity tensor in two dimensions: oblique, rectangular, square, and isotropic. In two dimensions, orthogonal transformations are either reflections or rotations. The proof is based on identification of constraints imposed by reflections and rotations on the elasticity tensor, and it simply employs elementary tools from trigonometry, making the proof accessible to a broad audience. For completeness, we identify the sets of transformations (rotations and reflections) for each symmetry class and report the corresponding equations of motions in classical linear elasticity.

42 ENGINEERING↗

DOE OSTI2019

Elastic strain tensor of zirconium hydrides in Zr2.5%Nb pressure tubes by synchrotron X-ray diffraction

Zirconium alloys are used in fuel cladding and structural components of nuclear power plants. Hydrogen enters the Zr matrix during plant operation and precipitates as hydride particles that degrade the mechanical properties of the alloy, limiting service life. Knowledge of the stress state within hydride precipitates is important to understand stress-induced degradation mechanisms such as delayed hydride cracking, but no direct quantification has yet been reported in the literature. Here, measurements are reported of the average elastic strain tensor within δ zirconium hydride precipitates in Zr2.5%Nb pressure tube material from CANDU power plants. Complete intensity and strain pole figures for the hydride were obtained by synchrotron X-ray diffraction experiments on specimens with hydrogen contents ranging from ~100 wt p.p.m. hydrogen to nearly 100% δ-hydride. Zirconium hydride precipitates by a process involving a martensitic transformation, with two hydride variants possible from a single α-Zr grain. A synthetic model of the hydride crystallographic texture allowed the interpretation of the measured strain pole figures and quantification of the elastic strain tensor for both texture components. It was found that the two variants appear in nearly equal proportion but with different stress states, differing in the sign of the shear strain components (~±3000 µ$\epsilon$). This difference is possibly associated with the shear movement of Zr atoms during the phase transformation. This suggests that hydride clusters are composed of stacks of smaller hydrides in alternating hydride variants. Stresses were estimated from a set of rather uncertain hydride elastic constants. Overall, both variants showed compressive strains along the tube axial direction (~5000 µ$\epsilon$). For low hydrogen concentrations, the hydrides' stress tensor is dominated by compressive stresses of ~300 MPa along the axial direction, probably caused by the elongated morphology of hydride clusters along this direction, and variant-dependent shear stresses of ~±100 MPa, probably from the shear movement of the Zr atoms involved in the phase transformation.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Determination of the Complete Spin Density Distribution in 13 C-Labeled Protein-Bound Radical Intermediates Using Advanced 2D Electron Paramagnetic Resonance Spectroscopy and Density Functional Theory

Determining the complete electron spin density distribution for protein-bound radicals, even with advanced pulsed electron paramagnetic resonance (EPR) methods, is a formidable task. Here we present a strategy to overcome this problem combining multifrequency HYSCORE and ENDOR measurements on site-specifically 13 C-labeled samples with DFT calculations on model systems. As a demonstration of this approach, pulsed EPR experiments are performed on the primary Q A and secondary Q B ubisemiquinones of the photosynthetic reaction center from Rhodobacter sphaeroides 13C-labeled at the ring and tail positions. Despite the large number of nuclei interacting with the unpaired electron in these samples, two-dimensional X- and Q-band HYSCORE and orientation selective Q-band ENDOR resolve and allow for a characterization of the eight expected 13 C resonances from significantly different hyperfine tensors for both semiquinones. From these results we construct, for the first time, the most complete experimentally determined maps of the s- and p π -orbital spin density distributions for any protein organic cofactor radical to date. This work lays a foundation for understanding the relationship between the electronic structure of semiquinones and their functional properties, and introduces new techniques for mapping out the spin density distribution that are readily applicable to other systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Permutation-adapted complete and independent basis for atomic cluster expansion descriptors

In many recent applications, particularly in the field of atom-centered descriptors for interatomic potentials, tensor products of spherical harmonics have been used to characterize complex atomic environments. When coupled with a radial basis, the atomic cluster expansion (ACE) basis is obtained. However, symmetrization with respect to both rotation and permutation results in an overcomplete set of ACE descriptors with linear dependencies occurring within blocks of functions corresponding to particular generalized Wigner symbols. All practical applications of ACE employ semi-numerical constructions to generate a complete, fully independent basis. While computationally tractable, the resultant basis cannot be expressed analytically, is susceptible to numerical instability, and thus has limited reproducibility. Here we present a procedure for generating explicit analytic expressions for a complete and independent set of ACE descriptors. The procedure uses a coupling scheme that is maximally symmetric w.r.t. permutation of the atoms, exposing the permutational symmetries of the generalized Wigner symbols, and yields a permutation-adapted rotationally and permutationally invariant basis (PA-RPI ACE). Theoretical support for the approach is presented, as well as numerical evidence of completeness and independence. A summary of explicit enumeration of PA-RPI functions up to rank 6 and polynomial degree 32 is provided. The PA-RPI blocks corresponding to particular generalized Wigner symbols may be either larger or smaller than the corresponding blocks in the simpler rotationally invariant basis. Finally, we demonstrate that basis functions of high polynomial degree persist under strong regularization, indicating the importance of not restricting the maximum degree of basis functions in ACE models a priori.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1991

Navier-Stokes computation of compressible turbulent flows with a second order closure

The objective was the development of a complete second order closure for wall bounded flows, including all components of the dissipation rate tensor and a numerical solution procedure for the resulting system of equations. The main topics discussed are the closure of the pressure correlations and the viscous destruction terms in the dissipation rate equations and the numerical solution scheme based on a block-tridiagonal solver for the nine equations required for the prediction of plane or axisymmetric flows.

Dingus, C.↗

NASA NTRS1981

Superconducting tensor gravity gradiometer for satellite geodesy and inertial navigation

A sensitive gravity gradiometer can provide much needed gravity data of the earth and improve the accuracy of inertial navigation. Superconductivity and other properties of materials at low temperatures can be used to obtain a sensitive, low-drift gravity gradiometer; by differencing the outputs of accelerometer pairs using superconducting circuits, it is possible to construct a tensor gravity gradiometer which measures all the in-line and cross components of the tensor simultaneously. Additional superconducting circuits can be provided to determine the linear and angular acceleration vectors. A tensor gravity gradiometer with these features is being developed for satellite geodesy. The device constitutes a complete package of inertial navigation instruments with angular and linear acceleration readouts as well as gravity signals.

Paik, H. J.↗

DOE OSTI2021

Electric dipole moment constraints on CP-violating heavy-quark Yukawas at next-to-leading order

Electric dipole moments are sensitive probes of new phases in the Higgs Yukawa couplings. We calculate the complete two-loop QCD anomalous dimension matrix for the mixing of CP-odd scalar and tensor operators and apply our results for a phenomenological study of CP violation in the bottom and charm Yukawa couplings. We find large shifts of the induced Wilson coefficients at next-to-leading-logarithmic order. Using the experimental bound on the electric dipole moments of the neutron and mercury, we update the constraints on CP-violating phases in the bottom and charm quark Yukawas.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Characterization and visualization of grain boundary disconnections

We introduce a method to visualize dislocations along grain boundaries at the atomic level. It uses an atomic-level Nye tensor, representing the dislocation density. To calculate the Nye tensor at grain boundaries, we extend the Hartley-Mishin strain gradient calculation to the displacement shift complete lattice. We show that the method is effective in visualizing disconnections and the dislocation content of grain boundary phase junctions in body-centered cubic tungsten, as well as face-centered cubic copper. In addition, we use the method to characterize the morphology of a two-dimensional grain boundary phase nucleus in a symmetric tilt grain boundary in tungsten. This method can be applied to both bulk dislocations and grain boundary disconnections, which makes it ideal for studying the interactions and reactions of bulk dislocations with grain boundaries, and grain boundary disconnections.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A finite-strain rate- and pressure-dependent constitutive framework for analyzing shock compression behavior of cemented tungsten carbides to 100 GPa

In the present study a thermodynamically-consistent finite-strain rate-and-pressure-dependent constitutive framework is implemented to analyze the shock-compression behavior of cemented tungsten carbides to 100 GPa. Central to this framework is the use of logarithmic strain with a set of invariant basis that allow the Cauchy stress tensor to be expressed as a sum of three response terms that are mutually orthogonal, thus permitting a complete separation of the deviatoric and volumetric (pressure) response. An overstress viscoplasticity model that includes strain and strain rate hardening along with thermal softening is used to represent the deviatoric response, while a complete Mie-Grüneisen equation of state (EoS) is used to obtain the pressure response. Using this formulation, the shock-induced compression behavior of cemented tungsten carbide - obtained from planar plate impact experiments using a 30 mm powder gun to peak stresses of up to ~100 GPa - is analyzed to better understand the structure of the measured shock wave profiles and the associated in-material shock quantities. Of particular interest is the evolution of material inelasticity and strength, and temperature in the tungsten carbide samples during the shock compression process.

Cemented tungsten carbide↗

DOE OSTI2025

Spinor representations for fields with any spin: Lorentz tensor basis for operators and covariant multipole decomposition

This paper discusses a framework to parametrize and decompose operator matrix elements for particles with higher spin (j > 1/2) using chiral representations of the Lorentz group, i.e. the (j, 0) and (0, j) representations and their parity-invariant direct sum. Unlike traditional approaches that require imposing constraints to eliminate spurious degrees of freedom, these chiral representations contain exactly the 2j + 1 components needed to describe a spin-j particle. The central objects in the construction are the t-tensors, which are generalizations of the Pauli four-vector σ μ for higher spin. For the generalized spinors of these representations, we demonstrate how the algebra of the t-tensors allows to formulate a generalization of the Dirac matrix basis for any spin. For on-shell bilinears, we show that a set consisting exclusively of covariant multipoles of order 0 ≤ m ≤ 2j forms a complete basis. We provide explicit expressions for all bilinears of the generalized Dirac matrix basis, which are valid for any spin value. As a byproduct of our derivations we present an efficient algorithm to compute the t-tensor matrix elements. The formalism presented here paves the way to use a more unified approach to analyze the non-perturbative QCD structure of hadrons and nuclei across different spin values, with clear physical interpretation of the resulting distributions as covariant multipoles.

Angular momentum of light↗

NASA NTRS2006

Exploiting Quantum Resonance to Solve Combinatorial Problems

Quantum resonance would be exploited in a proposed quantum-computing approach to the solution of combinatorial optimization problems. In quantum computing in general, one takes advantage of the fact that an algorithm cannot be decoupled from the physical effects available to implement it. Prior approaches to quantum computing have involved exploitation of only a subset of known quantum physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of tensor-product decomposability of unitary evolution of many-particle quantum systems for physically simulating solutions to NP-complete problems (a class of problems that are intractable with respect to classical methods of computation). In this approach, reinforcement and selection of a desired solution would be executed by means of quantum resonance. Classes of NP-complete problems that are important in practice and could be solved by the proposed approach include planning, scheduling, search, and optimal design.

Zak, Michail↗

DOE OSTI2019

Quarterly Management Document – FY19, 4th Quarter, Physics-based Creep Simulations of Thick Section Welds in High Temperature and Pressure Applications

During the 4th quarter of FY19, diffusional creep effects, based on the local stress tensor, was incorporated into the modeling and simulation efforts on thick section welds of Alloy 740H. The model is now complete and addresses both dislocation-based creep as well as diffusional creep mechanisms. Preliminary result indicate the model is now capable of predicting a transition from secondary creep to tertiary creep. Calibration of the model using experimental creep data remains to be performed and will be done in the first quarter of FY20.

36 MATERIALS SCIENCE↗

NASA NTRS1995

Large eddy simulations of compressible turbulent flows

An evaluation of existing models for Large Eddy Simulations (LES) of incompressible turbulent flows has been completed. LES is a computation in which the large, energy-carrying structures to momentum and energy transfer is computed exactly, and only the effect of the smallest scales of turbulence is modeled. That is, the large eddies are computed and the smaller eddies are modeled. The dynamics of the largest eddies are believed to account for most of sound generation and transport properties in a turbulent flow. LES analysis is based on an observation that pressure, velocity, temperature, and other variables are the sum of their large-scale and small-scale parts. For instance, u(i) (velocity) can be written as the sum of bar-u(i) and u(i)-prime, where bar-u(i) is the large-scale and u(i)-prime is the subgrid-scale (SGS). The governing equations for large eddies in compressible flows are obtained after filtering the continuity, momentum, and energy equations, and recasting in terms of Favre averages. The filtering operation maintains only large scales. The effects of the small-scales are present in the governing equations through the SGS stress tensor tau(ij) and SGS heat flux q(i). The mathematical formulation of the Favre-averaged equations of motion for LES is complete.

Porter-Locklear, Freda↗

DOE OSTI2018

Calculating Trajectories Associated With Solute Transport in a Heterogeneous Medium

Here, we present a trajectory-based technique for calculating solute transport in a porous medium that has several advantages over existing methods. Unlike streamlines, the extended trajectories are influenced by each of the important parameters governing transport, including molecular diffusion and transverse dispersion. The approach is complete and does not require any additional techniques, such as operator splitting or particle tracking, in order to account for the full dispersion tensor. The semianalytic expressions make it clear how the flow field, the concentration distribution, and the dispersion tensor contribute to the velocity field of an injected solute. The equations are valid for an arbitrary porous medium, including those with rapid spatial variations in properties, overcoming limitations faced by previous approaches based upon asymptotic techniques. A test on a layered model with sharp boundaries indicates that the extended trajectories are compatible with the results of a numerical simulator and differ from streamlines. We also describe a new form of the dispersion tensor that incorporates a known asymmetry. The trajectories indicate that the modifications of the dispersion tensor lead to more focused transport within regions of high conductivity. The trajectories are used to define a semianalytic relationship between solute travel times and variations in solute velocities along a path that may be used for tomographic imaging. In an application to the injection of a radioactive tracer into a Berea sandstone core, monitored using micropositron emission tomographic (micro-PET) observations, the sensitivities are used to map the spatial variations of permeability within the core.

42 ENGINEERING↗

NASA NTRS1994

On the prediction of free turbulent jets with swirl using a quadratic pressure-strain model

Data from free turbulent jets both with and without swirl are used to assess the performance of the pressure-strain model of Speziale, Sarkar and Gatski which is quadratic in the Reynolds stresses. Comparative predictions are also obtained with the two versions of the Launder, Reece and Rodi model which are linear in the same terms. All models are used as part of a complete second-order closure based on the solution of differential transport equations for each non-zero component of the Reynolds stress tensor together with an equation for the scalar energy dissipation rate. For non-swirling jets, the quadratic model underestimates the measured spreading rate of the plane jet but yields a better prediction for the axisymmetric case without resolving the plane jet/round jet anomaly. For the swirling axisymmetric jet, the same model accurately reproduces the effects of swirl on both the mean flow and the turbulence structure in sharp contrast with the linear models which yield results that are in serious error. The reasons for these differences are discussed.

Younis, Bassam A.↗

NASA NTRS1976

On the equation of state for an electron gas in an intense magnetic field

In this paper we derive the equation of state for a relativistic electron gas imbedded in a static homogeneous magnetic field of arbitrary strength. The derivation is based on the evaluation of the energy-momentum tensor and the use of Dirac's equation for such a problem. Contrary to a derivation presented several years ago, the present derivation is completely gauge-invariant. We also show how to recover, in an exact manner, the perfect gas law for the case of weak magnetic fields.

Canuto, V.↗

NASA NTRS1994

Squeezed states and graviton-entropy production in the early universe

Squeezed states are a very useful framework for the quantum treatment of tensor perturbations (i.e. gravitons production) in the early universe. In particular, the non equilibrium entropy growth in a cosmological process of pair production is completely determined by the associated squeezing parameter and is insensitive to the number of particles in the initial state. The total produced entropy may represent a significant fraction of the entropy stored today in the cosmic blackbody radiation, provided pair production originates from a change in the background metric at a curvature scale of the Planck order. Within the formalism of squeezed thermal states it is also possible to discuss the stimulated emission of gravitons from an initial thermal bath, under the action of the cosmic gravitational background field. We find that at low energy the graviton production is enhanced, if compared with spontaneous creation from the vacuum; as a consequence, the inflation scale must be lowered, in order not to exceed the observed CMB quadrupole anisotropy. This effect is important, in particular, for models based on a symmetry-breaking transition which require, as initial condition, a state of thermal equilibrium at temperatures higher than the inflation scale and in which inflation has a minimal duration.

Giovannini, Massimo↗

DOE OSTI2020

Report for Department of State (DoS) V-Fund Project "Tying Moment Tensor Solutions to Explosive Yield"

The goal of this study was to use U.S. nuclear explosions with known source parameters (yield, depth, shot point material and/or parameters) to determine moment-derived yield estimates. This work has been accomplished by performing full moment tensor solutions using regional network data from the LLNL network, and other regional broadband stations. As part of this study, we have calculated solutions for 130 U.S. nuclear explosions and 12 additional chemical explosions. We then take several approaches to using moment tensors to estimate yield, considering both the full and isotropic moment tensors, doing straight regression analysis on the whole dataset, then successively refining the calibration with additional information about material and overburden. We have also tried a completely new approach of using the seismic moment to help estimate the radiated seismic energy and tying this to yield through a seismic efficiency. Results appear to be promising, but more work might be required to make this more useful in an operational sense.

58 GEOSCIENCES↗