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At least 973 records · Page 54

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DOE OSTI2020

Assessing the effect of regularization on the molecular properties predicted by SCAN and self-interaction corrected SCAN meta-GGA

Recent regularization of the SCAN meta-GGA functional (rSCAN) has simplified the numerical complexities of the SCAN functional, alleviating SCAN's stringent demand on the numerical integration grids to some extent. The regularization of rSCAN, however, results in the breaking of some constraints such as the uniform electron gas limit, the slowly varying density limit, and coordinate scaling of the iso-orbital indicator. Here, we assess the effects of regularization on the electronic, structural, vibrational, and magnetic properties of molecules by comparing the SCAN and rSCAN predictions. The properties studied include atomic energies, atomization energies, ionization potentials, electron affinities, barrier heights, infrared intensities, dissociation and reaction energies, spin moments of molecular magnets, and isomer ordering of water clusters. Our results show that rSCAN requires less dense numerical grids and gives very similar results to those of SCAN for all properties examined with the exception of atomization energies, which are worsened in rSCAN. We also examine the performance of self-interaction-corrected (SIC) rSCAN with respect to SIC-SCAN using the Perdew–Zunger (PZ) SIC method. The PZSIC method uses orbital densities to compute one-electron self-interaction errors and places an even more stringent demand on numerical grids. Our results show that SIC-rSCAN gives marginally better performance than SIC-SCAN for almost all properties studied in this work with numerical grids that are on average half or less as dense as that needed for SIC-SCAN.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2000

Low-dimensional Representation of Error Covariance

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.

Tippett, Michael K.↗

DOE OSTI2016

Effective computation of stochastic protein kinetic equation by reducing stiffness via variable transformation

The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated round-off errors. For such situation, we provide a method of reducing stiffness of the stochastic protein kinetic equation by means of a kind of variable transformation. Theoretical and numerical analysis show effectiveness of this method. Its generalization to a more general class of stochastic differential equation models is also discussed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations I: Derivation and algorithms

We propose a dynamically bi-orthogonal method (DyBO) to solve time dependent stochastic partial differential equations (SPDEs). The objective of our method is to exploit some intrinsic sparse structure in the stochastic solution by constructing the sparsest representation of the stochastic solution via a bi-orthogonal basis. It is well-known that the Karhunen–Loeve expansion (KLE) minimizes the total mean squared error and gives the sparsest representation of stochastic solutions. However, the computation of the KL expansion could be quite expensive since we need to form a covariance matrix and solve a large-scale eigenvalue problem. The main contribution of this paper is that we derive an equivalent system that governs the evolution of the spatial and stochastic basis in the KL expansion. Unlike other reduced model methods, our method constructs the reduced basis on-the-fly without the need to form the covariance matrix or to compute its eigendecomposition. In the first part of our paper, we introduce the derivation of the dynamically bi-orthogonal formulation for SPDEs, discuss several theoretical issues, such as the dynamic bi-orthogonality preservation and some preliminary error analysis of the DyBO method. We also give some numerical implementation details of the DyBO methods, including the representation of stochastic basis and techniques to deal with eigenvalue crossing. In the second part of our paper [11], we will present an adaptive strategy to dynamically remove or add modes, perform a detailed complexity analysis, and discuss various generalizations of this approach. An extensive range of numerical experiments will be provided in both parts to demonstrate the effectiveness of the DyBO method.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1984

Resistance-foil strain-gage technology as applied to composite materials

A general review of existing strain-gage technologies as applied to orthotropic-composite materials is given. The specific topics addressed are gage-bonding procedures, transverse-sensitivity effects, errors due to gage misalignment, and temperature-compensation methods. The discussion is supplemented by numerical examples where appropriate. It is shown that the orthotropic behavior of composites can result in experimental error which would not be expected based on practical experience with isotropic materials. In certain cases, the transverse sensitivity of strain gages and/or slight gage misalignment can result in strain-measurement errors exceeding 50 percent.

Tuttle, M. E.↗

NASA NTRS1991

An iterative implicit diagonally-dominant factorization algorithm for solving the Navier-Stokes equations

Presented here is an algorithm for solving the multidimensional unsteady Navier-Stokes equations for compressible flows. It is based on a diagonally-dominant approximate factorization procedure. The factorization error and the timewise linearization error associated with this procedure are reduced by performing Newton-type inner iterations at each time step. The inviscid fluxes are evaluated by the fourth-order central differencing scheme amended with a numerical dissipation directly proportional to the entire dissipative part of the truncation error intrinsic to the third order biased upwind scheme. The important features of the proposed solution are elucidated by the numerical results of the convection of a vortex and the backward-facing step flows.

Chen, Shu-Cheng↗

DOE OSTI2018

Evaluating a Simple Fracturing Criterion for a Hydraulic Fracture Crossing Stress and Stiffness Contrasts

Hydraulic fracture height containment is a critical issue in the development of unconventional reservoirs. The extent of fracture height growth depends on a variety of factors, particularly stress and stiffness contrasts between adjacent layers. Accurate simulation of fracture growth and containment requires a reliable fracturing criterion. The virtual crack closure technique (VCCT) is a widely used method for computing energy release rate. However, it is based on the assumption that a small crack extension does not significantly alter the state of the crack tip, which is generally not the case when a fracture crosses strong stress and/or stiffness contrasts. In this work, we assess the applicability and accuracy of a modified virtual crack closure technique (MVCCT) for a fluid-driven fracture in breaking through interfaces with significant stress and/or stiffness contrasts, through comparisons with analytical and reference numerical solutions. Here, the results show that significant error could occur when the fracture tip is very near or at stress/stiffness interfaces. However, this error is localized to the interface and proves to be inconsequential to the predicted penetration depth into the rock layer beyond the interface. Finally, this study validates the applicability of MVCCT in 3D hydraulic fracturing simulation in strongly heterogeneous rock formations.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Effect of Fragile Speckle Patterns on Accuracy of Digital Volume Correlation

Due to challenges in generating high-quality 3D speckle patterns for Digital Volume Correlation (DVC) strain measurements, DVC experiments often utilize the intrinsic texture and contrast of composite microstructures. One common deficiency of these natural speckle patterns is their poor durability under large deformations, which can lead to decorrelation and inaccurate strain measurements. Using syntactic foams as a model material, the effects of speckle pattern degradation on the accuracy of DVC displacement and strain measurements are assessed with both experimentally-acquired and numerically-generated images. It is shown that measurement error can be classified into two regimes as a function of the percentage of markers that have disappeared from the speckle pattern. For minor levels of damage beneath a critical level of damage, displacement and strain error remained near the noise floor of less than 0.05 voxels and 100 με, respectively; above this level, error rapidly increased to unacceptable levels above 0.2 voxels and 10,000 με. This transition occurred after 30%–40% of the speckles disappeared, depending on characteristics of the speckle pattern and its degradation mechanisms. Furthermore, these results suggest that accurate DVC measurements can be obtained in many types of fragile materials despite severe damage to the speckle pattern.

42 ENGINEERING↗

DOE OSTI2020

Discrete element modeling of switchgrass particles under compression and rotational shear

Switchgrass is a perennial herbaceous plant regarded as a biomass energy crop in the United States for its highadaptability and yield potential. Processing and handling of switchgrass particles are challenging due to the erratic mechanical and flow behavior originating from their intrinsic particulate properties. Here, we present a bonded-sphere discrete element model designed specifically for switchgrass particles. The model simultaneously captures three key particulate features, i.e., fibrous particle shapes, a wide range of particle sizes, and particle deformability. Realistic yet computationally efficient particle shape templates are created based on the image analysis data of switchgrass specimens. A fitting procedure is proposed to ensure both the particle width and length distributions are captured, a unique requirement for fibrous particles. Two full-scale numerical models, i.e., a uniaxial compression model and a Schulze ring shear model, are developed using information fromphysical experiments. The model is calibrated using experimental data of chopped-small switchgrass specimens, and then, is validated using data of chopped-large specimens in both compression and ring-shear tests. Numerical results show that the numerical models capture bulk densities accurately (with an error of 3%) while slightly underestimate the bulk friction angle. Furthermore, an extensive sensitivity analysis reveals that (1) switchgrass particles with rougher edges (due to different processing techniques) exhibit a higher shear strength and a lower flowability; (2) stiffer particles yield a lower bulk density (up to 21% lower) compared to more deformable particles, indicating particle deformability should be incorporated when modeling biomass flow in a preprocessing system.

09 BIOMASS FUELS↗

DOE OSTI2026

Parametric reduced order models for graded lattice structures

Graded lattice structures, characterized by smoothly varying mechanical properties, hold significant promise for optimizing material distribution in advanced engineering applications. However, accurately modeling these structures poses substantial computational challenges due to the continuous geometric variations within their unit cells. Here, to address these challenges, this paper introduces a novel Efficient Reduced Order Model (EROM) that integrates the Matrix Discrete Empirical Interpolation Method (MDEIM) and Discrete Empirical Interpolation Method (DEIM) with polynomial regression to efficiently manage geometric parametrization in lattice structures. Unlike traditional reduced order models (ROMs) that require extensive precomputed libraries for each geometric configuration, our approach enables continuous geometric variations through a flexible algebraic formulation, significantly reducing computational costs while preserving high accuracy. The method constructs projection matrices for individual unit cells that can be efficiently assembled into global systems, leveraging the repetitive nature of lattice structures. Numerical studies demonstrate that our EROM achieves displacement errors below 1% and von Mises stress prediction errors below 4%, coupled with computational speedups exceeding two orders of magnitude compared to full-order simulations. The proposed method's modularity and scalability make it particularly suitable for design optimization and real-time simulation of functionally graded lattice structures, with applications spanning aerospace to biomedical engineering.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Improvements to a class of hybrid methods for radiation transport: Nyström reconstruction and defect correction methods

In this study, two modifications are introduced for improving the accuracy, versatility, and robustness of a class of hybrid methods for radiation transport. In general, such methods are constructed by splitting the radiative flux into collided and uncollided components to which low- and high-resolution angular approximations are applied, respectively. In this work we focus on discrete ordinates discretizations of high and low order. The first modification we introduce changes the way in which the collided component is mapped into the uncollided component at the end of each time step in a simulation. The new mapping is a Nyström-type reconstruction that is applicable to arbitrary discrete ordinates quadratures, is guaranteed to preserve positivity of the solution provided that all ordinate weights are positive, is significantly more accurate than previous methods, and can be readily extended to other discretizations such as moment methods, finite element methods, and diffusion approximations. The second modification leverages integral deferred correction (IDC) to iteratively correct for the splitting error introduced by the inconsistency in angular discretization between the collided and uncollided components, in addition to improving the accuracy of the low-order temporal error that is treated by traditional IDC methods. Numerical tests in one- and two-dimensional geometries are used to demonstrate the increased accuracy and efficiency of the proposed modifications. It is found that the two techniques combined yield methods with solution accuracy and memory requirements comparable to that of monolithic discrete ordinates methods while reducing runtime by as much as a factor of between two and ten, depending on the problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Constraint energy minimizing generalized multiscale finite element method for multi-continuum Richards equations

In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced order methods are demanded. Combining these techniques with nonlinearity, we will consider in this paper a dual-continuum model which is generalized as a multi-continuum model for a coupled system of nonlinear Richards equations as unsaturated flows, in complex heterogeneous fractured porous media; and we will solve it by a novel multiscale approach utilizing the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). In particular, such a nonlinear system will be discretized in time and then linearized by Picard iteration (whose global convergence is proved theoretically). Subsequently, we tackle the resulting linearized equations by the CEM-GMsFEM and obtain proper offline multiscale basis functions to span the multiscale space (which contains the pressure solution). More specifically, we first introduce two new sources of samples, and the GMsFEM is used over each coarse block to build local auxiliary multiscale basis functions via solving local spectral problems, that are crucial for detecting high-contrast channels. Second, per oversampled coarse region, local multiscale basis functions are created through the CEM as constrainedly minimizing an energy functional. Various numerical tests for our approach reveal that the error converges with the coarse-grid size and that only few oversampling layers as well as basis functions are needed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Benchmarking magnetised three-wave coupling for laser backscattering: analytic solutions and kinetic simulations

Understanding magnetised laser–plasma interactions is important for controlling magneto-inertial fusion experiments and developing magnetically assisted radiation and particle sources. For nanosecond pulses at non-relativistic intensities, interactions are dominated by coherent three-wave interactions, whose nonlinear coupling coefficients became known only recently when waves propagate at oblique angles with the magnetic field. In this paper, backscattering coupling coefficients predicted by warm-fluid theory are benchmarked using particle-in-cell simulations in one spatial dimension, and excellent agreements are found for a wide range of plasma temperatures, magnetic field strengths and laser propagation angles, when the interactions are mediated by electron-dominant hybrid waves. Systematic comparisons between theory and simulations are made possible by a rigorous protocol. On the theory side, the initial boundary value problem of linearised three-wave equations is solved, and the transient-time solutions allow the effects of growth and damping to be distinguished. On the simulation side, parameters are carefully chosen and calibration runs are performed to ensure that comparisons are well controlled. Fitting simulation data to analytical solutions yields numerical growth rates that match theory predictions within error bars. Although warm-fluid theory is found to be valid for a wide parameter range, genuine kinetic effects have also been observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2019

New Basis Set Exchange: An Open, Up-to-date Resource for the Molecular Sciences Community

In computational quantum chemistry, the basis set is a fundamental input to many types of simulations, and the choice of basis set can have dramatic effects on both the accuracy and performance of the simulation. Due to this fundamental nature, basis sets have been developed starting at the beginning of the computational chemistry field, and extending to the present day, with new basis sets taking into account new theories and methods now accessible due to increases in computing power. Practically, computations are most comparable when they use the same basis set. However, early distribution channels often led to differing incorporation of basis sets indifferent computational chemistry codes, harming reproducibility and introducing errors in calculations that can go unnoticed. Such errors can be due to many causes, including transcription errors, neglecting publication of the full precision of numerical values, updated values not being incorporated in a timely manner, or development of an ‘improved’ version by different developers that retains the same name as the original basis set. Therefore, there was a need to store basis sets in a central location and make them easily and freely accessible by any researcher. The Basis Set Exchange (BSE) is widely considered by the field to be such a resource.

basis set, ab initio, web application, web interfa↗

DOE OSTI2015

Model and particle-in-cell simulation of ion energy distribution in collisionless sheath

In this paper, we propose a self-consistent theoretical model, which is described by the ion energy distributions (IEDs) in collisionless sheaths, and the analytical results for different combined dc/radio frequency (rf) capacitive coupled plasma discharge cases, including sheath voltage errors analysis, are compared with the results of numerical simulations using a one-dimensional plane-parallel particle-in-cell (PIC) simulation. The IEDs in collisionless sheaths are performed on combination of dc/rf voltage sources electrodes discharge using argon as the process gas. The incident ions on the grounded electrode are separated, according to their different radio frequencies, and dc voltages on a separated electrode, the IEDs, and widths of energy in sheath and the plasma sheath thickness are discussed. The IEDs, the IED widths, and sheath voltages by the theoretical model are investigated and show good agreement with PIC simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2019

Disconnected covariance of 2-point functions in large-scale structure

Optimal analyses using the 2-point functions of large-scale structure probes require accurate covariance matrices. A covariance matrix of the 2-point function comprises the disconnected part and the connected part. While the connected covariance only becomes important on small scales, the disconnected covariance is dominant on large scales, where the survey window has a significant impact. In this work, we develop an analytical method to compute the disconnected covariance, accounting for the window effect. Derived under the flat-sky approximation, our formalism is applicable to wide surveys by swapping in the curved-sky window functions. Our method works for both the power spectrum and the correlation function, and applies to the covariances of various probes including the multipoles and the wedges of 3D clustering, the angular and the projected statistics of clustering and shear, as well as the cross covariances between different probes. We verify the analytic covariance against the sample covariance from the galaxy mock simulations in two test cases: (1) the power spectrum multipole covariance, and (2) the joint covariance of the projected correlation function and the correlation function multipoles. Our method achieve good agreement with the mocks, while at a negligible computational cost. Unlike mocks, our analytic covariance is free of sampling noise, which often leads to numerical problems and the need to inflate the errors. In addition, our method can use the best-fit power spectrum as input, in contrast to the standard procedure of using a fiducial model that may deviate significantly from the truth. We also show that a naive diagonal power spectrum covariance underestimates the signal-to-noise ratio compared to our analytic covariance. The code that accompanies this paper is available at https://github.com/eelregit/covdisc.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Ab Initio Bulk Free Energy Surface of Proper Ferroelectrics

We report a systematic and accurate approach for deriving the bulk free energy surface (FES), a function of temperature, polarization, and strain, from the first-principles density functional theory (DFT) of proper ferroelectrics. The core of our approach is the metadynamics algorithm that extracts the polarization dependence of the FES from all-atom molecular dynamics simulations without an a priori ansatz. The rest of the FES is derived from the metadynamics trajectories that span the relevant phase space. We demonstrate our approach in the case of lead titanate. The errors across the phase transition, due to DFT numerics, all-atom molecular dynamics, and free energy evaluation by enhanced sampling, can be systematically controlled and are of the order of 1 meV/atom. The accuracy of the resulting ab initio FES is only limited by the adopted functional approximation of DFT.

Xie, Pinchen [Lawrence Berkeley National Laborator↗

DOE OSTI2019

Digitizing gauge fields: Lattice Monte Carlo results for future quantum computers

We report that in the near-future noisy intermediate-scale quantum (NISQ) era of quantum computing technology, applications of quantum computing will be limited to calculations of very modest scales in terms of the number of qubits used. The need to represent numeric quantities using limited resources leads to digitization errors which must be taken into account. As a first step towards quantum simulations of realistic high-energy physics problems, we explore classically the effects of digitizing elements of the $\mathrm{SU}(2)$ gauge group to a finite set. We consider several methods for digitizing the group, finding the best performance from an action-preserving projection onto a mesh. Working in (3+1) dimensions, we find that using $\sim 7$ (qu)bits to represent each $\mathrm{SU}(2)$ gauge link induces a digitization error on the order of $10\%$ in short-distance observables and $2\%$ in long-distance observables. Promisingly, our results indicate that each $\mathrm{SU}(2)$ gauge link can be represented by $\mathcal{O}(10)$ (qu)bits, from which we estimate that a $16^3$ $\mathrm{SU}(2)$ lattice could be simulated with no more than $\mathcal{O}(10^5)$ (qu)bits. Lastly, our results on digitization are also of interest as a form of lossy compression that could be used in high-performance classical computing to alleviate communications bottlenecks.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗