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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

An Analytical Solution for the Initiation and Early Progression of Fretting Wear in Spherical Contacts

Abstract This article derives analytical solutions to calculate the wear volume at the initiation of fretting motion and its early progression over the first few oscillation cycles. The Archard-based model considers a deformable hemisphere that is contact with a deformable flat block. The material pairs investigated are special alloys, the Inconel 617/Incoloy 800H, and Inconel 617/Inconel 617. The analytical study begins with a unidirectional frictional sliding contact, where the local interfacial sliding distance and the nominal sliding distance at the initiation of gross slip are derived. The obtained analytical expressions for unidirectional sliding are then used to derive the corresponding wear volume for the initiation and early progression of gross slip and the wear volume for a general fretting cycle under elastic conditions. These analytical derivations are all verified by the finite element analysis (FEA). The FEA method and the analytical solutions render virtually identical results for both similar and dissimilar material pairs. The effects of plasticity on the wear volume under elastic–plastic conditions are also investigated. It is found that the fretting wear volumes obtained from the FEA simulations, which include plasticity, are close to those obtained from the analytical expressions for purely elastic regimes. All the results are presented in normalized forms, which can be easily generalized and applied to three-dimensional fretting wear of other material pairs.

Engineering↗
DOE OSTI2018

An arc-length method for controlled cohesive crack propagation using high-order XFEM and Irwin’s crack closure integral

Numerical modeling of cohesive crack growth in quasi-brittle materials is challenging, primarily due to the combination of (i) nonlinearity associated with the fracture process zone (FPZ), (ii) arbitrary directions to which a crack may propagate, and (iii) snap-back or snap-through instabilities encountered in the response of the structure. To address these challenges, here we propose a novel arc-length method that can follow the equilibrium path of cohesive crack propagation. The proposed approach is based on the extended finite element method (XFEM) with scalar high-order enrichment functions and Irwin’s crack closure integral, which allows for direct control of the applied loads necessary to propagate cohesive cracks. This is achieved by augmenting a constraint equation written in terms of stress intensity factors (SIFs), and expressed explicitly in terms of the enriched degrees of freedom, which is an attractive feature achieved with Irwin’s integral, since SIFs can be written in closed-form. Note that singular enrichments are active in an unstable crack propagation state and automatically vanish in stable crack configurations. Furthermore, to propagate cracks in arbitrary directions, we employ a maximum circumferential stress criterion implemented by (i) direct usage of the SIFs, and by (ii) a new stress-based nonlocal implementation of this principle. Various benchmark problems including pure mode I and mixed-mode fracture are solved to demonstrate the predictive capability of the present framework for cohesive crack modeling.

42 ENGINEERING↗
DOE OSTI2021

Parallel projection—An improved return mapping algorithm for finite element modeling of shape memory alloys

Here, we present a novel finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to resolve. Finite element analysis methods, which rely on Gauss quadrature integration schemes, must solve two sets of coupled differential equations: one at the global level and the other at the local, i.e. Gauss point level. In contrast to the conventional return mapping algorithm, which solves these two sets of coupled differential equations separately using a nested Newton procedure, we propose a scheme to solve the local and global differential equations simultaneously. In the process we also derive closed-form expressions used to update the internal/constitutive state variables, and unify the popular closest-point and cutting plane methods with our formulas. Numerical testing indicates that our method allows for larger thermomechanical loading steps and provides increased computational efficiency, over the standard return mapping algorithm.

42 ENGINEERING↗
DOE OSTI2018

A fourth-order accurate finite volume method for ideal MHD via upwind constrained transport

Here we present a fourth-order accurate finite volume method for the solution of ideal magnetohydrodynamics (MHD). The numerical method combines high-order quadrature rules in the solution of semi-discrete formulations of hyperbolic conservation laws with the upwind constrained transport (UCT) framework to ensure that the divergence-free constraint of the magnetic field is satisfied. A novel implementation of UCT that uses the piecewise parabolic method (PPM) for the reconstruction of magnetic fields at cell corners in 2D is introduced. The resulting scheme can be expressed as the extension of the second-order accurate constrained transport (CT) Godunov-type scheme that is currently used in the Athena astrophysics code. After validating the base algorithm on a series of hydrodynamics test problems, we present the results of multidimensional MHD test problems which demonstrate formal fourth-order convergence for smooth problems, robustness for discontinuous problems, and improved accuracy relative to the second-order scheme.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Feynman diagrams for matter wave interferometry

We introduce a new theoretical framework based on Feynman diagrams to compute phase shifts in matter wave interferometry. The method allows for analytic computation of higher order quantum corrections, beyond the traditional semi-classical approximation. These additional terms depend on the finite size of the initial matter wavefunction and/or have higher order dependence on ℏ. We apply the method to compute the response of matter wave interferometers to power law potentials and potentials with an arbitrary spatial dependence. The analytic expressions are validated by comparing to numerical simulations, and estimates are provided for the scale of the quantum corrections to the phase shift response to the gravitational field of the earth, anharmonic trapping potentials, and gravitational fields from local proof masses. We also find that for certain experimentally feasible parameters, these corrections are large enough to be measured and could lead to systematic errors if they are not mitigated. We find that to first order in a spatially dependent potential, quantum corrections vanish when the initial matter wavepacket has spherical symmetry and the potential satisfies Laplace's equation. We anticipate these quantum corrections will be especially important for trapped matter wave interferometers and for free-space matter wave interferometers in the presence of proof masses. These interferometers are becoming increasingly sensitive tools for mobile inertial sensing, gravity surveying, tests of gravity and its interplay with quantum mechanics, and searches for dark energy.

Glick, Jonah [Northwestern U.; Fermilab] (ORCID:00↗
DOE OSTI2018

Analytic atomic gradients in the fermi‐löwdin orbital self‐interaction correction

We derived, implemented, and thoroughly tested the complete analytic expression for atomic forces, consisting of the Hellmann‐Feynman term and the Pulay correction, for the Fermi‐Löwdin orbital self‐interaction correction (FLO‐SIC) method. Analytic forces are shown to be numerically accurate through an extensive comparison to forces obtained from finite differences. Using the analytic forces, equilibrium structures for a small set of molecules were obtained. This work opens the possibility of routine self‐interaction free geometrical relaxations of molecules using the FLO‐SIC method. © 2018 Wiley Periodicals, Inc.

Trepte, Kai↗
DOE OSTI2018

Integrable Variable Dissipation Systems on the Tangent Bundle of a Multi-Dimensional Sphere and Some Applications

This paper is a survey of integrable cases in dynamics of a multi-dimensional rigid body under the action of a nonconservative force field. We review both new results and results obtained earlier. Problems examined are described by dynamical systems with so-called variable dissipation with zero mean. The problem of the search for complete sets of transcendental first integrals of systems with dissipation is quite topical; a large number of works are devoted to it. We introduce a new class of dynamical systems that have a periodic coordinate. Due to the existence of nontrivial symmetry groups of such systems, we can prove that these systems possess variable dissipation with zero mean, which means that on the average for a period with respect to the periodic coordinate, the dissipation in the system is equal to zero, although in various domains of the phase space, either energy pumping or dissipation can occur. Based on the facts obtained, we analyze dynamical systems that appear in the dynamics of a multi-dimensional rigid body and obtain a series of new cases of complete integrability of the equations of motion in transcendental functions, which can be expressed through a finite combination of elementary functions. As applications, we study dynamical equations of motion arising in the study of the plane and spatial dynamics of a rigid body interacting with a medium and also a possible generalization of the obtained methods to the study of general systems arising in the qualitative theory of ordinary differential equations, in the theory of dynamical systems, and also in oscillation theory.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Kinetic simulations of collision-less plasmas in open magnetic geometries

Laboratory plasmas in open magnetic geometries can be found in many different applications such as (a) scrape-of-layer (SOL) and divertor regions in toroidal confinement fusion devices, (b) linear divertor simulators, (c) plasma-based thrusters and (d) magnetic mirrors etc. A common feature of these plasma systems is the need to resolve, in addition to velocity space, at least one physical dimension (e.g. along flux lines) to capture the relevant physics. In general, this requires a kinetic treatment. Fully kinetic particle-in-cell (PIC) simulations can be applied but at the expense of large computational effort. A common way to resolve this is to use a hybrid approach: kinetic ions and fluid electrons. In the present work, the development of a hybrid PIC computational tool suitable for open magnetic geometries is described which includes (a) the effect of non-uniform magnetic fields, (b) finite fully-absorbing boundaries for the particles and (c) volumetric particle sources. Analytical expressions for the momentum transport in the paraxial limit are presented with their underlying assumptions and are used to validate the results from the PIC simulations. A general method is described to construct discrete particle distribution functions in a state of mirror-equilibrium. This method is used to obtain the initial state for the PIC simulation. Collisionless simulations in a mirror geometry are performed. The results show that the effect of magnetic compression is correctly described and momentum is conserved. The self-consistent electric field is calculated and is shown to modify the ion velocity distribution function in a manner consistent with analytic theory. Based on this analysis, the ion distribution function is understood in terms of a loss-cone distribution and an isotropic Maxwell-Boltzmann distribution driven by a volumetric plasma source. Finally, the inclusion of a Monte Carlo based Fokker-Planck collision operator is discussed in the context of future work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Optimal local truncation error method for 3-D elasticity interface problems

The paper deals with a new effective numerical technique on unfitted Cartesian meshes for simulations of heterogeneous elastic materials. Here, we develop the optimal local truncation error method (OLTEM) with 27- point stencils (similar to those for linear finite elements) for the 3-D time-independent elasticity equations with irregular interfaces. Only displacement unknowns at each internal Cartesian grid point are used. The interface conditions are added to the expression for the local truncation error and do not change the width of the stencils. The unknown stencil coefficients are calculated by the minimization of the local truncation error of the stencil equations and yield the optimal second order of accuracy for OLTEM with the 27-point stencils on unfitted Cartesian meshes. A new post-processing procedure for accurate stress calculations has been developed. Similar to basic computations it uses OLTEM with the 27-point stencils and the elasticity equations. The post-processing procedure can be easily extended to unstructured meshes and can be independently used with existing numerical techniques (e.g., with finite elements). Numerical experiments show that at an accuracy of 0.1% for stresses, OLTEM with the new post-processing procedure significantly (by 10 5 -10 9 times) reduces the number of degrees of freedom compared to linear finite elements. OLTEM with the 27-point stencils yields even more accurate results than high-order finite elements with wider stencils.

42 ENGINEERING↗
DOE OSTI2026

Beyond Contrast Transfer: Spectral SNR as a Finite-Dose Metric for STEM Phase Retrieval

The contrast transfer function (CTF) is widely used to evaluate phase retrieval methods in scanning transmission electron microscopy (STEM), including center-of-mass imaging, parallax imaging, direct ptychography, and iterative ptychography. However, the CTF reflects only the maximum usable signal, neglecting the effects of finite electron fluence and the Poisson-limited nature of detection. As a result, it can significantly overestimate practical performance, especially in low-dose regimes. Here, we employ the spectral signal-to-noise ratio (SSNR), as a finite-dose statistical framework to evaluate the recoverable signal as a function of spatial frequency. Using numerical reconstructions of white-noise objects, we show that center-of-mass, parallax, and direct ptychography exhibit dose-independent SSNRs, with close-form analytic expressions. In contrast, iterative ptychography exhibits a surprising dose dependence: at low fluence, its SSNR converges to that of direct ptychography; at high fluence, it saturates at a value consistent with the maximum detective quantum efficiency predicted by recent quantum Fisher information bounds. The results highlight the limitations of CTF-based evaluation and motivate SSNR as a more accurate, finite-dose metric for assessing STEM phase retrieval methods.

STEM phase retrieval↗
DOE OSTI2021

On the in-plane vibrations and electromechanical resonance characteristics of non-uniformly polarized rectangular piezoelectric wafers: Selective mode-type excitation and specific mode enhancement

Here, we investigate the in-plane vibrations and electromechanical resonance characteristics of non-uniformly polarized rectangular piezoelectric wafers. Non-uniform polarization is represented as a non-uniform electromechanical coupling coefficient using a polarization function. Governing equations are derived for the forced in-plane vibrations of a thin wafer under the assumption of generalized plane stress. The effect of non-uniform polarization is explicitly obtained in the forcing terms of the governing equations. These equations are then recast into a variational weak form that is then solved using the finite element method to obtain the displacement fields for different modes. The electromechanical response of a non-uniformly polarized piezoelectric wafer is derived in terms of the out-of-plane displacement profile on the surface of the wafer. Using the derived analytical expression, a necessary and sufficient condition for the presence/absence of a vibrational mode in the electromechanical impedance spectrum is obtained. Based on this condition, criteria for selective mode-type excitation and specific mode enhancement of vibrational modes in the electromechanical impedance spectrum are postulated. Selective mode-type excitation of in-plane extensional and shear modes is demonstrated for a square wafer and that of in-plane bending modes is demonstrated for a rectangular wafer. Specific mode enhancement is demonstrated for both square and rectangular wafers. In addition, it is also demonstrated how the criteria can be used to suppress specific vibrational modes in the electromechanical impedance spectrum. The proposed methodology of using non-uniformly polarized piezoelectric wafers finds application in the design of single element transducers with multi-frequency operation, frequency-tuned receivers/sensors, acoustic holograms, designing acoustic beams of prescribed shape/lobes, and other non-traditional applications such as information storage.

36 MATERIALS SCIENCE↗
DOE OSTI2017

SQDFT: Spectral Quadrature method for large-scale parallel O ( N ) Kohn–Sham calculations at high temperature

We present SQDFT: a large-scale parallel implementation of the Spectral Quadrature (SQ) method for $\mathscr{O}(N)$ Kohn–Sham Density Functional Theory (DFT) calculations at high temperature. Specifically, we develop an efficient and scalable finite-difference implementation of the infinite-cell Clenshaw–Curtis SQ approach, in which results for the infinite crystal are obtained by expressing quantities of interest as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw–Curtis quadrature rules. We demonstrate the accuracy of SQDFT by showing systematic convergence of energies and atomic forces with respect to SQ parameters to reference diagonalization results, and convergence with discretization to established planewave results, for both metallic and insulating systems. Here, we further demonstrate that SQDFT achieves excellent strong and weak parallel scaling on computer systems consisting of tens of thousands of processors, with near perfect $\mathscr{O}(N)$ scaling with system size and wall times as low as a few seconds per self-consistent field iteration. Finally, we verify the accuracy of SQDFT in large-scale quantum molecular dynamics simulations of aluminum at high temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Giant Graviton Expansion from Bubbling Geometry: Discreteness from Quantized Geometry

The superconformal index of half-BPS states in N = 4 supersymmetric Yang-Mills with gauge group U⁡(N) admits an expansion in terms of giant gravitons, J N (q) = J ∞ ⁡(q)⁢Σ$^{∞}_{m=0}$ q m⁢N ⁢ J^ m ⁡(q), where m is the number of giant gravitons and J ∞ ⁡(q) is the graviton index. The expansion can be viewed as the implementation of trace relations for finite N. We derive this expansion directly in supergravity from the class of half-BPS solutions due to Lin, Lunin, and Maldacena in type IIB supergravity. The moduli space of these configurations can be quantized using covariant quantization methods. We show how this quantization leads to the precise expression for the expansion in terms of giant gravitons. Our proposal provides a derivation of the giant graviton expansion directly in terms of quantized supergravity degrees of freedom, and it recovers discrete data via quantum geometries that are classically nonsmooth.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A practical approach to calculating magnetic Johnson noise for precision measurements

Magnetic Johnson noise is an important consideration for many applications involving precision magnetometry, and its significance will only increase in the future with improvements in measurement sensitivity. The fluctuation–dissipation theorem can be utilized to derive analytic expressions for magnetic Johnson noise in certain situations, but when used in conjunction with finite element analysis tools, the combined approach is particularly powerful as it provides a practical means to calculate the magnetic Johnson noise arising from conductors of arbitrary geometry and permeability. In this paper, we demonstrate this method to be one of the most comprehensive approaches presently available to calculate thermal magnetic noise. In particular, its applicability is shown to not be limited to cases where the noise is evaluated at a point in space but also can be expanded to include cases where the magnetic field detector has a more general shape, such as a finite-size loop, a gradiometer, or a detector that consists of a polarized atomic species trapped in a volume. Furthermore, some physics insights gained through studies made using this method are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Assessing Critical Conditions for Scour Near Obstructions using Bed Shear, Particle Onset of Motion Balances, and CFD-DEM Modeling of Granular Beds

Computational Fluid Dynamics combined with a Discrete Element Method is one of the computational methods that can be used to model multiphase flows. In this method various phases, gas and liquid or solid, are present in the same computational domain. The local averaged Navier–Stokes equations determine the flow of the continuous phase fluid and are solved using the traditional CFD finite volume approach. DEM is based on a Lagrangian formulation, which solves the equations of motion, expressed in ordinary differential equations, for representative particles as they move in space and time. The interactions between the continuous fluid phase and discrete solid phase are modeled with the use of Newton’s laws of motion via drag force. The particles interact with each other and with the boundaries of the fluid continuum, and the resulting contact forces are included in the equations of motion. The properties of solid particles and boundaries are treated as elastic bodies, with specified density, elastic modulus, and Poisson’s ratio. Particle shapes may vary from single spherical particles to more complex-shaped composite particles. The particles may be introduced into the domain by random or structured injection at a point, surface, or volume, depending on the application. More details on the formulation can be found in the Simcenter STAR-CCM+ User’s Manual and OpenFOAM website.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Adaptive Data-Driven Deep-Learning Surrogate Model for Frontal Polymerization in Dicyclopentadiene

Frontal polymerization (FP) is a self-sustaining curing process that enables rapid and energy-efficient manufacturing of thermoset polymers and composites. Computational methods conventionally used to simulate the FP process are time-consuming, and repeating simulations are required for sensitivity analysis, uncertainty quantification, or optimization of the manufacturing process. Here, in this work, we develop an adaptive surrogate deep-learning model for FP of dicyclopentadiene (DCPD), which predicts the evolution of temperature and degree of cure orders of magnitude faster than the finite-element method (FEM). The adaptive algorithm provides a strategy to select training samples efficiently and save computational costs by reducing the redundancy of FEM-based training samples. The adaptive algorithm calculates the residual error of the FP governing equations using automatic differentiation of the deep neural network. A probability density function expressed in terms of the residual error is used to select training samples from the Sobol sequence space. The temperature and degree of cure evolution of each training sample are obtained by a 2D FEM simulation. The adaptive method is more efficient and has a better prediction accuracy than the random sampling method. With the well-trained surrogate neural network, the FP characteristics (front speed, shape, and temperature) can be extracted quickly from the predicted temperature and degree-of-cure fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

An adjoint-based optimization method for jointly inverting heterogeneous material properties and fault slip from earthquake surface deformation data

SUMMARY Analysis of tectonic and earthquake-cycle associated deformation of the crust can provide valuable insights into the underlying deformation processes including fault slip. How those processes are expressed at the surface depends on the lateral and depth variations of rock properties. The effect of such variations is often tested by forward models based on a priori geological or geophysical information. Here, we first develop a novel technique based on an open-source finite-element computational framework to invert geodetic constraints directly for heterogeneous media properties. We focus on the elastic, coseismic problem and seek to constrain variations in shear modulus and Poisson’s ratio, proxies for the effects of lithology and/or temperature and porous flow, respectively. The corresponding nonlinear inversion is implemented using adjoint-based optimization that efficiently reduces the cost function that includes the misfit between the calculated and observed displacements and a penalty term. We then extend our theoretical and numerical framework to simultaneously infer both heterogeneous Earth’s structure and fault slip from surface deformation. Based on a range of 2-D synthetic cases, we find that both model parameters can be satisfactorily estimated for the megathrust setting-inspired test problems considered. Within limits, this is the case even in the presence of noise and if the fault geometry is not perfectly known. Our method lays the foundation for a future reassessment of the information contained in increasingly data-rich settings, for example, geodetic GNSS constraints for large earthquakes such as the 2011 Tohoku-oki M9 event, or distributed deformation along plate boundaries as constrained from InSAR.

Geochemistry & Geophysics↗
DOE OSTI2024

Effective rationality for local unitary invariants of mixed states of two qubits

Abstract We calculate the field of rational local unitary invariants for mixed states of two qubits, by employing methods from algebraic geometry. We prove that this field is rational (i.e. purely transcendental), and that it is generated by nine algebraically independent polynomial invariants. We do so by constructing a relative section, in the sense of invariant theory, whose Weyl group is a finite abelian group. From this construction, we are able to give explicit expressions for the generating invariants in terms of the Bloch matrix representation of mixed states of two qubits. We also prove similar rationality results for the local unitary invariants of symmetrically mixed states of two qubits. We also provide a sketch of how to generalize our results to the case of an arbitrary number of qubits. Our results apply to both complex-valued and real-valued invariants.

Physics↗