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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Lattice Instability during Solid-Solid Structural Transformations under a General Applied Stress Tensor: Example of Si I → Si II with Metallization

Here, the density functional theory was employed to study the stress-strain behavior and elastic instabilities during the solid-solid phase transformation (PT) when subjected to a general stress tensor, as exemplified for semiconducting Si I and metallic Si II, where metallization precedes the PT, so stressed Si I can be a metal. The hydrostatic PT occurs at 76 GPa, while under uniaxial loading it is 11 GPa (3.7 GPa mean pressure), 21 times lower. The Si I→Si II PT is described by a critical value of the phase-field’s modified transformation work, and the PT criterion has only two parameters given six independent stress elements. Our findings reveal novel, more practical synthesis routes for new or known high-pressure phases under predictable nonhydrostatic loading, where competition of instabilities can serve for phase selection rather than free energy minima used for equilibrium processing.

42 ENGINEERING↗
DOE OSTI2021

Deep Learning Predicts Stress–Strain Relations of Granular Materials Based on Triaxial Testing Data

This study presents an AI-based constitutive modelling framework wherein the prediction model directly learns from triaxial testing data by combining discrete element modelling (DEM) and deep learning. A constitutive learning strategy is proposed based on the generally accepted frame-indifference assumption in constructing material constitutive models. The low-dimensional principal stress-strain sequence pairs, measured from discrete element modelling of triaxial testing, are used to train recurrent neural networks, and then the predicted principal stress sequence is augmented to other high-dimensional or general stress tensor via coordinate transformation. Through detailed hyperparameter investigations, it is found that long short-term memory (LSTM) and gated recurrent unit (GRU) networks have similar prediction performance in constitutive modelling problems, and both satisfactorily predict the stress responses of granular materials subjected to a given unseen strain path. Furthermore, the unique merits and ongoing challenges of data-driven constitutive models for granular materials are discussed.

42 ENGINEERING↗
DOE OSTI2022

Surface stress tensor and junction conditions on a rotating null horizon

The general form of the surface stress tensor of an infinitesimally thin shell located on a rotating null horizon is derived, when different interior and exterior geometries are joined there. Even though the induced metric on the surface must be the same approached from either side, the first derivatives of the metric need not be. Such discontinuities lead to a Dirac δ-distribution in the Einstein tensor localized on the horizon. For a general stationary axisymmetric geometry the surface stress tensor can be expressed in terms of two geometric invariants that characterize the surface, namely the discontinuities [κ] and [J] of the surface gravity κ and angular momentum density J. The Komar energy and angular momentum are given in coordinates adapted to the Killing symmetries, and the surface contributions to each determined in terms of [κ] and [J] . Guided by these, a simple modification of the original Israel junction conditions is verified directly from the Einstein tensor density to give the correct finite result for the surface stress, when the normal n to the surface is allowed to tend continuously to a null vector. The relation to Israel’s original junction conditions, which fail on null surfaces, is given. The modified junction conditions are suitable to the matching of a rotating “black hole” exterior to any interior geometry joined at the Kerr null horizon surface, even when the surface normal is itself discontinuous and the Barrabès-Israel formalism is also inapplicable. This joining on a rotating null horizon is purely of the matter shell type and does not contain a propagating gravitational shock wave.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Extension of the flow-rate-of-strain tensor formulation of plasma rotation theory to non-axisymmetric tokamaks

A systematic formalism for the calculation of rotation in non-axisymmetric tokamaks with 3D magnetic fields is described. The Braginskii Ωτ-ordered viscous stress tensor formalism, generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry, and the resulting fluid moment equations provide a systematic formalism for the calculation of toroidal and poloidal rotation and radial ion flow in tokamaks in the presence of various non-axisymmetric “neoclassical toroidal viscosity” mechanisms. The relation among rotation velocities, radial ion particle flux, ion orbit loss, and radial electric field is discussed, and the possibility of controlling these quantities by producing externally controllable toroidal and/or poloidal currents in the edge plasma for this purpose is suggested for future investigation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1991

Shock waves and the Ffowcs Williams-Hawkings equation

The expansion of the double divergence of the generalized Lighthill stress tensor, which is the basis of the concept of the role played by shock and contact discontinuities as sources of dipole and monopole sound, is presently applied to the simplest transonic flows: (1) a fixed wing in steady motion, for which there is no sound field, and (2) a hovering helicopter blade that produces a sound field. Attention is given to the contribution of the shock to sound from the viewpoint of energy conservation; the shock emerges as the source of only the quantity of entropy.

Isom, Morris P.↗
DOE OSTI2022

Brown-York charges at null boundaries

The Brown-York stress tensor provides a means for defining quasilocal gravitational charges in subregions bounded by a timelike hypersurface. We consider the generalization of this stress tensor to null hypersurfaces. Such a stress tensor can be derived from the on-shell subregion action of general relativity associated with a Dirichlet variational principle, which fixes an induced Carroll structure on the null boundary. The formula for the mixed-index tensor T i j takes a remarkably simple form that is manifestly independent of the choice of auxiliary null vector at the null surface, and we compare this expression to previous proposals for null Brown-York stress tensors. The stress tensor we obtain satisfies a covariant conservation equation with respect to any connection induced from a rigging vector at the hypersurface, as a result of the null constraint equations. For transformations that act covariantly on the boundary structures, the Brown-York charges coincide with canonical charges constructed from a version of the Wald-Zoupas procedure. For anomalous transformations, the charges differ by an intrinsic functional of the boundary geometry, which we explicity verify for a set of symmetries associated with finite null hyper-surfaces. Applications of the null Brown-York stress tensor to symmetries of asymptotically flat spacetimes and celestial holography are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

EGS Stimulation Design with Uncertainty Quantification at the EGS Collab Site

Engineering a robust hydraulic connection between wells is one of the most difficult aspects of enhanced geothermal systems (EGS). Designing and constructing such hydraulic connections requires and understanding of the in situ state of stress and the heterogeneities and discontinuities that naturally exist and may control the stimulation. Even with comprehensive stress and formation characterization programs substantial uncertainty remains in these key parameters. This is especially the case in high-temperature EGS environments where drilling conditions are often difficult and a far fewer logging and testing options are available. This paper presents a new approach for explicitly quantifying the uncertainties in the state of stress using a Bayesian Markov Chain Monte Carlo method. This approach produces a probability distribution for the stress tensor, including a general 3D orientation, that reflects the uncertainties in all the observations or indicators used to constrain the stress state. This method is demonstrated on the characterization data for the EGS Collab Experiment 2 site. The output of the analysis is used to guide the design of the planned stimulations. In the case of research projects like EGS Collab, explicitly quantifying the uncertainties in the stress state allow for more rigorous hypothesis testing by allowing conclusions drawn from the experiments to be interpreted in the context of the uncertain knowledge about conditions in the test bed.

Burghardt, Jeffrey A.↗
DOE OSTI2014

Viscous damping of toroidal angular momentum in tokamaks

The Braginskii viscous stress tensor formalism was generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry in order to provide a representation for the viscous damping of toroidal rotation in tokamaks arising from various “neoclassical toroidal viscosity” mechanisms. In the process, it was verified that the parallel viscosity contribution to damping toroidal angular momentum still vanishes even in the presence of toroidal asymmetries, unless there are 3D radial magnetic fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

THE GENERAL RELATIVISTIC EQUATIONS OF RADIATION HYDRODYNAMICS IN THE VISCOUS LIMIT

We present an analysis of the general relativistic Boltzmann equation for radiation, appropriate to the case where particles and photons interact through Thomson scattering, and derive the radiation energy-momentum tensor in the diffusion limit with viscous terms included. Contrary to relativistic generalizations of the viscous stress tensor that appear in the literature, we find that the stress tensor should contain a correction to the comoving energy density proportional to the divergence of the four-velocity, as well as a finite bulk viscosity. These modifications are consistent with the framework of radiation hydrodynamics in the limit of large optical depth, and do not depend on thermodynamic arguments such as the assignment of a temperature to the zeroth-order photon distribution. We perform a perturbation analysis on our equations and demonstrate that as long as the wave numbers do not probe scales smaller than the mean free path of the radiation, the viscosity contributes only decaying, i.e., stable, corrections to the dispersion relations. The astrophysical applications of our equations, including jets launched from super-Eddington tidal disruption events and those from collapsars, are discussed and will be considered further in future papers.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Lattice instability during phase transformations under multiaxial stress: Modified transformation work criterion

A continuum/atomistic approach for predicting lattice instability during crystal-crystal phase transformations (PTs) is developed for the general loading with an arbitrary stress tensor and large strains. It is based on a synergistic combination of the generalized Landau-type theory for PTs and molecular dynamics (MD) simulations. The continuum approach describes the entire dissipative transformation process in terms of an order parameter, and the general form of the instability criterion is derived utilizing the second law of thermodynamics. The feedback from MD allowed us to present the instability criterion for both direct and reverse PTs in terms of the critical value of the modified transformation work, which is linear in components of the true stress tensor. It was calibrated by MD simulations for direct and reverse PTs between semiconducting silicon Si i and metallic Si ii phases under just two different stress states. Then, it describes hundreds of MD simulations under various combinations of three normal and three shear stresses. Finally, in particular, the atomistic simulations show that the effects of all three shear stresses along cubic axes on lattice instability of Si i are negligible, which is in agreement with our criterion.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

Cosmological backreaction in higher-derivative gravity expansions

We calculate a general effective stress-energy tensor induced by cosmological inhomogeneity in effective theories of gravity where the action is Taylor-expandable in the Riemann tensor and covariant derivatives of the Riemann tensor. This is of interest as an effective fluid that might provide an alternative to the cosmological constant, but it also applies to gravitational waves. We use an adaptation of Green and Wald's weak-averaging framework, which averages over perturbations in the field equation where the perturbation length scales are small compared to the averaging scale. In this adaptation, the length scale of the effective theory, 1/ M , is also taken to be small compared with the averaging scale. This ensures that the perturbation length scales remain in fixed proportion to the length scale of the effective theory as the cosmological averaging scale is taken to be large. We find that backreaction from higher-derivative terms in the effective action can continue to be important in the late universe, given a source of sufficiently high-frequency metric perturbations. This backreaction might also provide a window on exotic particle physics in the far ultraviolet.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1986

Viscosity and the Chew-Goldberger-Low equations in the solar corona

A general discussion of the dominant terms in the stress tensor in a magnetized plasma such as the solar corona is presented. The importance of dissipative terms such as electrical resistivity, heat conduction, and interspecies collisions is assessed. For average coronal conditions, the proton stress tensor is found to reduce to the dominant terms in the classical expression for the viscous stress. The classical expression can fail in the transition region, however. In the diffusion region of reconnection, classical viscosity will be appropriate if the resistivity is very large, so that the diffusion region is broad, but in that case the viscous heating is small compared to the resistive heating. On the other hand, the more general expression for the stress tensor is required if the diffusion region is thin; the stress tensor will be important in this case. The electron stress tensor is also considered, and it is shown how the classical expression for electron viscosity can fail in the transition region and lower corona.

Hollweg, J. V.↗
DOE OSTI2016

Action principle for Coulomb collisions in plasmas

In this study, an action principle for Coulomb collisions in plasmas is proposed. Although no natural Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1996

Element Library for Three-Dimensional Stress Analysis by the Integrated Force Method

The Integrated Force Method, a recently developed method for analyzing structures, is extended in this paper to three-dimensional structural analysis. First, a general formulation is developed to generate the stress interpolation matrix in terms of complete polynomials of the required order. The formulation is based on definitions of the stress tensor components in term of stress functions. The stress functions are written as complete polynomials and substituted into expressions for stress components. Then elimination of the dependent coefficients leaves the stress components expressed as complete polynomials whose coefficients are defined as generalized independent forces. Such derived components of the stress tensor identically satisfy homogenous Navier equations of equilibrium. The resulting element matrices are invariant with respect to coordinate transformation and are free of spurious zero-energy modes. The formulation provides a rational way to calculate the exact number of independent forces necessary to arrive at an approximation of the required order for complete polynomials. The influence of reducing the number of independent forces on the accuracy of the response is also analyzed. The stress fields derived are used to develop a comprehensive finite element library for three-dimensional structural analysis by the Integrated Force Method. Both tetrahedral- and hexahedral-shaped elements capable of modeling arbitrary geometric configurations are developed. A number of examples with known analytical solutions are solved by using the developments presented herein. The results are in good agreement with the analytical solutions. The responses obtained with the Integrated Force Method are also compared with those generated by the standard displacement method. In most cases, the performance of the Integrated Force Method is better overall.

Kaljevic, Igor↗
DOE OSTI2017

Bounds on OPE coefficients from interference effects in the conformal collider

We apply the average null energy condition to obtain upper bounds on the three-point function coefficients of stress tensors and a scalar operator, ⟨TTO⟩, in general CFTs. We also constrain the gravitational anomaly of U(1) currents in four-dimensional CFTs, which are encoded in three-point functions of the form ⟨TTJ⟩. In theories with a large N AdS dual we translate these bounds into constraints on the coefficient of a higher derivative bulk term of the form ∫Φ W 2 . We speculate that these bounds also apply in de-Sitter. In this case our results constrain inflationary observables, such as the amplitude for chiral gravity waves that originate from higher derivative terms in the Lagrangian of the form Φ W W*.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

T Duality and T T ¯ -like Deformations of Sigma Models

We initiate the study of the interplay between T duality and classical stress tensor deformations in two-dimensional sigma models. We first show that a general Abelian T duality commutes with the T T ¯ deformation, which can be engineered by a gravitational dressing. Then, by using an auxiliary field formulation of stress tensor deformations of the principal chiral model (PCM), we prove that non-Abelian T duality and arbitrary T T ¯ -like flows also commute for theories in this class. We argue that all such auxiliary field deformations of both the PCM and its T dual are classically integrable. Published by the American Physical Society 2025

Bielli, Daniele (ORCID:0009000640034768)↗
DOE OSTI2019

Eigensensitivity analysis of subgrid-scale stresses in large-eddy simulation of a turbulent axisymmetric jet

The study of complex turbulent flows by means of large-eddy simulation approaches has become increasingly popular in many scientific and engineering applications. The underlying filtering operation of the approach enables to significantly reduce the spatial and temporal resolution requirements by means of representing only large-scale motions. However, the small-scale stresses and their effects on the resolved flow field are not negligible, and therefore require additional modeling. As a consequence, the assumptions made in the closure formulations become potential sources of model-form uncertainty that can impact the quantities of interest. The objective of this work, thus, is to perform a model-form sensitivity analysis in large-eddy simulations of an axisymmetric turbulent jet following an eigenspace-based strategy recently proposed. The approach relies on introducing perturbations to the decomposed subgrid-scale stress tensor within a range of physically plausible values. These correspond to discrepancy in magnitude (trace), anisotropy (eigenvalues) and orientation (eigenvectors) of the normalized, small-scale stresses with respect to a given tensor state, such that propagation of their effects can be assessed. As a result, the generality of the framework with respect to the six degrees of freedom of the small-scale stress tensor makes it also suitable for its application within data-driven techniques for improved subgrid-scale modeling.

42 ENGINEERING↗