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At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Magnetic phase diagram of a two-orbital model for bilayer nickelates with varying doping

Motivated by the recently discovered high-T c bilayer nickelate superconductor La 3⁢ Ni 2 ⁢O 7 , we comprehensively research a bilayer 2×2×2 cluster for different electronic densities n by using the Lanczos method. We also employ the random-phase approximation to quantify the first magnetic instability with increasing Hubbard coupling strength, also varying n. Based on the spin structure factor S(q), we have obtained a rich magnetic phase diagram in the plane defined by n and U/W, at fixed Hund coupling, where U is the Hubbard strength and W the bandwidth. We have observed numerous states, such as A-AFM, Stripes, G-AFM, and C-AFM. At half-filling, n=2 (two electrons per Ni site, corresponding to N=16 electrons), the canonical superexchange interaction leads to a robust G-AFM state (π,π,π) with antiferromagnetic couplings both in-plane and between layers. By increasing or decreasing electronic densities, ferromagnetic tendencies emerge from the “half-empty” and “half-full” mechanisms, leading to many other interesting magnetic tendencies. In addition, the spin-spin correlations become weaker both in the hole or electron doping regions compared with half-filling. At n=1.5 (or N=12), density corresponding to La 3 ⁢Ni 2 ⁢O 7 , we obtained the “Stripe 2” ground state (antiferromagnetic coupling in one in-plane direction, ferromagnetic coupling in the other, and antiferromagnetic coupling along the z axis) in the 2×2×2 cluster. In addition, we obtained a much stronger AFM coupling along the z axis than the magnetic coupling in the xy plane. The random-phase approximation calculations with varying n give very similar results as Lanczos, even though both techniques are based on quite different procedures. Additionally, a state with q/π=(0.6,0.6,1) close to the E-phase wavevector is found in our RPA calculations by slightly reducing the filling to n=1.25, possibly responsible for the E-phase SDW recently observed in experiments. In conclusion, our predictions can be tested by chemically doping La 3 ⁢Ni 2 ⁢O 7 .

36 MATERIALS SCIENCE↗
DOE OSTI2022

Learning high-dimensional parametric maps via reduced basis adaptive residual networks

We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is beneficial to have a compact parametrization in order to ameliorate the ill-posedness of the neural network training problem. By linearly restricting high-dimensional maps to informed reduced bases of the inputs, one can compress high-dimensional maps in a constructive way that can be used to detect appropriate basis ranks, equipped with rigorous error estimates. A scalable neural network learning framework is thus to learn the nonlinear compressed reduced basis mapping. Unlike the reduced basis construction, however, neural network constructions are not guaranteed to reduce errors by adding representation power, making it difficult to achieve good practical performance. Inspired by recent approximation theory that connects ResNets to sequential minimizing flows, we present an adaptive ResNet construction algorithm. This algorithm allows for depth-wise enrichment of the neural network approximation, in a manner that can achieve good practical performance by first training a shallow network and then adapting. We prove universal approximation of the associated neural network class for $L^2_v$ functions on compact sets. Our overall framework allows for constructive means to detect appropriate breadth and depth, and related compact parametrizations of neural networks, significantly reducing the need for architectural hyperparameter tuning. Numerical experiments for parametric PDE problems and a 3D CFD wing design optimization parametric map demonstrate that the proposed methodology can achieve remarkably high accuracy for limited training data, and outperformed other neural network strategies we compared against.

42 ENGINEERING↗
DOE OSTI2023

Effects of Size and Shape on the Tolerances for Misalignment and Probabilities for Successful Oriented Attachment of Nanoparticles

Oriented attachment (OA) of nanoparticles is an important pathway of crystal growth, but tools for quantitatively modeling OA are lacking. Here we present several simple models that relate the probability of achieving OA to basic geometric parameters such as particle size, shape, and lattice periodicity. A Moiré-domain model is applied to understand twist-misorientations between parallel surfaces, and it predicts that the range of twist angles yielding perfect OA is inversely related to the width of the contact area. This is confirmed and further developed using a surface functional model, which predicts how crystallographic registration forces drive the emergence of complex orientational energy landscapes. The energy landscapes are predicted to possess local minima that can trap particles in imperfect alignments, and these local minima become deeper and more numerous as the contact area increases, making OA more challenging for large particles. Further, a second set of models is presented to understand the sequence of events by which two crystallographic faces become co-planer after collision. We use a ‘central force approximation’ to quantitatively predict the odds of attaining coalignment between various faces when particles collide with random misalignments, and we show that in the absence of biasing forces, the probability of attaining alignment on a given face is roughly proportional to its solid angle as viewed from the center of the particle. The model predicts that OA is most favorable between well-faceted particles and becomes exceedingly unlikely for large spherical particles that express many microfacets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

An accurate, non-empirical method for incorporating decoherence into Ehrenfest dynamics

In mixed quantum-classical nonadiabatic molecular dynamics methods, the anchoring of the electronic wave function to a single nuclear geometry results in both quantitative and qualitative errors in the dynamics. In the context of both Ehrenfest and trajectory surface hopping methods, methods for incorporating decoherence are widely used to eliminate these errors. However, the accuracy of these methods often depends strongly on the parameterization of the decoherence time and/or other related quantities. Here, we present a refinement of the recently introduced collapse to a block (TAB) scheme for incorporating decoherence into Ehrenfest dynamics. The proposed approach incorporates an approximation to the history of the population dynamics and treats the coherence decay as Gaussian, rather than exponential. This method uses parameters that can be obtained from first principles, rather than empirical fitting. Application to one-dimensional models indicates excellent agreement with numerically exact simulations. We also introduce a second refinement to the TAB method: a robust linear least-squares algorithm for determining collapse probabilities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Random insights into the complexity of two-dimensional tensor network calculations

Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law and are the basis for classical simulations of ground states in two-dimensional (2d) condensed matter systems. However, rigorous results show that exactly computing observables from a 2d PEPS state is generically a computationally hard problem. Yet approximation schemes for computing properties of 2d PEPS are regularly used, and empirically seen to succeed, for a large subclass of (“not too entangled”) condensed matter ground states. Adopting the philosophy of random matrix theory, in this work, we analyze the complexity of approximately contracting a 2d random PEPS by exploiting an analytic mapping to an effective replicated statistical mechanics model that permits a controlled analysis at a large bond dimension. Through this statistical-mechanics lens, we argue that (i) although approximately sampling wave-function amplitudes of random PEPS faces a computational-complexity phase transition above a critical bond dimension, and (ii) one can generically efficiently estimate the norm and correlation functions for any finite bond dimension. Furthermore, these results are supported numerically for various bond-dimension regimes. It is an important open question whether the above results for random PEPS apply more generally also to PEPS representing physically relevant ground states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Rapid simulations of hyperspectral near-field images of three-dimensional heterogeneous surfaces – part II

The modeling of the near-field interaction in the scattering-type scanning near-field optical microscope (s-SNOM) is rapidly advancing, although an accurate yet versatile modeling framework that can be easily adapted to various complex situations is still lacking. In this work, we propose a time-efficient numerical scheme in the quasi-electrostatic limit to capture the tip-sample interaction in the near field. This method considers an extended tip geometry, which is a significant advantage compared to the previously reported method based on the point-dipole approximation. Using this formalism, we investigate, among others, nontrivial questions such as uniaxial and biaxial anisotropy in the near-field interaction, the relationship between various experimental parameters (e.g. tip radius, tapping amplitude, etc.), and the tip-dependent spatial resolution. The demonstrated method further sheds light on the understanding of the contrast mechanism in s-SNOM imaging and spectroscopy, while also representing a valuable platform for future quantitative analysis of the experimental observations.

Chen, Xinzhong (ORCID:0000000261033848)↗
DOE OSTI2022

Preconditioning for Hyper-reduction in Reduced Order Models

Many projection-based reduced order models (pROM) that utilize the governing equation and data to accelerate physical simulations can be applied to nonlinear dynamical systems. To avoid full order model (FOM) scale update for each time step, hyperreduction techniques are developed to sample high dimensional nonlinear terms. Our study aims to investigate if preconditioning the least-squares problem used for the nonlinear approximation can improve the robustness of the condition number of the problem while achieving high accuracy. In our study, we use the row-normalization matrix motivated by the Christoffel function as the preconditioner and solve the corresponding weighted least-squares problem. Numerical results for Lagrangian hydrodynamics examples are analyzed to explore how the preconditioner works compared to existing hyper-reduction techniques.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Characterizing Hydraulic Fracture Propagation Before Fracture Hits

Estimating the distance from hydraulic fracture tip to monitor well can be very useful for fracture characterization, well spacing optimization, and preventing parent-child well interference. Heart-shape signal is referred to as the extensional precursor of fracture hit recorded by cross-well strain measurements and can be served as a vital tool to make such estimation. This study incorporates the 3D Displacement Discontinuity Method to understand the impact of fracture geometry and monitor well offset on the heart-shape signal’s characteristics. Results from numerical simulation and analytical solutions reveal a strong linear correlation between the spatial extent of heart shape signal and fracture tip distance. This relationship was further developed to predict tip distance using field data from the Hydraulic Fracture Test Site 2. A reasonable approximation result from field data further validates the methodology. In addition, it is worth noting that the estimation accuracy depends on the ratio between fracture dimension and tip distance. The findings of this study offer a novel approach for real-time monitoring and characterizing hydraulic fracture propagation, which can be further used for well spacing optimization in unconventional and Enhanced Geothermal System reservoir development, as well as cap rock integrity monitoring for carbon sequestration projects.

Jin, Ge↗
DOE OSTI2022

Analysis of sparse recovery for Legendre expansions using envelope bound

We provide novel sufficient conditions for the uniform recovery of sparse Legendre expansions using ℓ 1 minimization, where the sampling points are drawn according to orthogonalization (uniform) measure. So far, conditions of the form m ≳ Θ 2 s x log factors have been relied on to determine the minimum number of samples m that guarantees successful reconstruction of s-sparse vectors when the measurement matrix is associated to an orthonormal system. However, in case of sparse Legendre expansions, the uniform bound Θ of Legendre systems is so high that these conditions are unable to provide meaningful guarantees. Here, in this paper, we present an analysis which employs the envelop bound of all Legendre polynomials instead, and prove a new recovery guarantee for s-sparse Legendre expansions, m ≳ Θs 2 x log factors, which is independent of Θ. Arguably, this is the first recovery condition established for orthonormal systems without assuming the uniform boundedness of the sampling matrix. The key ingredient of our analysis is an extension of chaining arguments, recently developed in Bourgain and Chkifa et al., to handle the envelope bound. Furthermore, our recovery condition is proved via restricted eigenvalue property, a less demanding replacement of restricted isometry property which is perfectly suited to the considered scenario. Along the way, we derive simple criteria to detect good sample sets. Our numerical tests show that sets of uniformly sampled points that meet these criteria will perform better recovery on average.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Effect of the volume fraction gradient on the phase interaction force model for disperse two-phase flows

In this work, the effects of the particle volume fraction gradient on fluid-particle interactions are studied. The phase interaction force is decomposed into three terms. For the first term, namely the symmetrized force density, we present theoretical reasoning and numerical evidence to assume that it is independent of the particle volume fraction gradient. The second term is the particle volume fraction gradient times a newly introduced diffusion stress. The third term is the divergence of the particle-fluid-particle (PFP) stress. If this assumption of independence of the particle volume fraction gradient for the first term can be verified, to the first order of the ratio of the mean distance between particles to the macroscopic lengthscale, all three terms can be studied and modeled in flows with uniform particle distributions. Models thus obtained are applicable to statistically inhomogeneous flows, with the second and third terms accounting for statistical inhomogeneity. To verify this assumption, numerical simulations of flows passing fixed arrays of particles are performed. Both uniform and nonuniform particle volume fractions are studied and compared for disperse multiphase flows with the particle Reynolds numbers ranging from 1 to 100, and particle volume fraction ranging from 1% to 26% in statistically steady states. It is found that the symmetrized force (first) term can be well approximated by the drag force obtained from studies of uniform flows. The diffusion stress is positive along the flow direction and negative in the directions perpendicular to the flow. In the case of moving particles, this stress could potentially cause particle aggregation in the flow direction and dispersion in the directions perpendicular to the flow. Finally, the diffusion stress is only important when there is a volume fraction gradient, while the PFP stress can be important in inhomogeneous flows with either nonuniform particle concentrations or nonuniform average relative velocities between the phases.

42 ENGINEERING↗
DOE OSTI2023

Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification

Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating the physical systems of interest with high-fidelity models is computationally expensive. This work proposes a context-aware multi-fidelity Monte Carlo method that optimally balances the costs of training low-fidelity models with the costs of Monte Carlo sampling. It generalizes the previously developed context-aware bi-fidelity Monte Carlo method to hierarchies of multiple models and to more general types of low-fidelity models. When training low-fidelity models, the proposed approach takes into account the context in which the learned low-fidelity models will be used, namely for variance reduction in Monte Carlo estimation, which allows it to find optimal trade-offs between training and sampling to minimize upper bounds of the mean-squared errors of the estimators for given computational budgets. This is in stark contrast to traditional surrogate modeling and model reduction techniques that construct low-fidelity models with the primary goal of approximating well the high-fidelity model outputs and typically ignore the context in which the learned models will be used in upstream tasks. Further, the proposed context-aware multi-fidelity Monte Carlo method applies to hierarchies of a wide range of types of low-fidelity models such as sparse-grid and deep-network models. Numerical experiments with the gyrokinetic simulation code Gene show speedups of up to two orders of magnitude compared to standard estimators when quantifying uncertainties in small-scale fluctuations in confined plasma in fusion reactors. This corresponds to a runtime reduction from 72 days to four hours on one node of the Lonestar6 supercomputer at the Texas Advanced Computing Center.

42 ENGINEERING↗
DOE OSTI2024

Algorithm 1049: The Delaunay Density Diagnostic

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the density of inputs is sufficient to identify the relevant variations in outputs—i.e., the “geometric scale” of the function—despite the fact that sampling density is closely tied to the success or failure of an approximation method. In this article, we introduce a general purpose, computational approach to detecting the geometric scale of real-valued functions over a fixed domain using a deterministic interpolation technique from computational geometry. The algorithm is intended to work on scalar data in moderate dimensions (2–10). Our algorithm is based on the observation that a sequence of piecewise linear interpolants will converge to a continuous function at a quadratic rate (in L 2 norm) if and only if the data are sampled densely enough to distinguish the feature from noise (assuming sufficiently regular sampling). We present numerical experiments demonstrating how our method can identify feature scale, estimate uncertainty in feature scale, and assess the sampling density for fixed (i.e., static) datasets of input–output pairs. Finally, we include analytical results in support of our numerical findings and have released lightweight code that can be adapted for use in a variety of data science settings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Shock Stabilization of the HLLC Riemann Solver for the Carbuncle Instability

The HLLC approximate Riemann solver improves upon the HLL Riemann solver by resolving contact discontinuities. This is a particularly desirable property for multi-material codes in which problems usually contain material interfaces. However, the HLLC solver is known to suffer from the carbuncle phenomenon, a numerical instability most apparent at grid-aligned shocks in multi-dimensional simulations. Many problems of interest, including high energy-density physics applications, require the accurate resolution of both material interfaces and hydrodynamic shocks. A variety of methods have been developed to cure this instability, with varying degrees of complexity. The objective of this work is to describe a simple approach to modify the HLLC Riemann solver and prevent the carbuncle instability. Here, the method is then demonstrated for assorted two-dimensional test problems known to exhibit the shock instability. The performance of the new solver is compared with that of the standard HLL and HLLC Riemann solvers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Nonlinear sparse Bayesian learning for physics-based models

This paper addresses the issue of overfitting while calibrating unknown parameters of over-parameterized physics-based models with noisy and incomplete observations. Here, a semi-analytical Bayesian framework of nonlinear sparse Bayesian learning (NSBL) is proposed to identify sparsity among model parameters during Bayesian inversion. NSBL offers significant advantages over machine learning algorithm of sparse Bayesian learning (SBL) for physics-based models, such as 1) the likelihood function or the posterior parameter distribution is not required to be Gaussian, and 2) prior parameter knowledge is incorporated into sparse learning (i.e. not all parameters are treated as questionable). NSBL employs the concept of automatic relevance determination (ARD) to facilitate sparsity among questionable parameters through parameterized prior distributions. The analytical tractability of NSBL is enabled by employing Gaussian ARD priors and by building a Gaussian mixture-model approximation of the posterior parameter distribution that excludes the contribution of ARD priors. Subsequently, type-II maximum likelihood is executed using Newton's method whereby the evidence and its gradient and Hessian information are computed in a semi-analytical fashion. We show numerically and analytically that SBL is a special case of NSBL for linear regression models. Subsequently, a linear regression example involving multimodality in both parameter posterior pdf and model evidence is considered to demonstrate the performance of NSBL in cases where SBL is inapplicable. Next, NSBL is applied to identify sparsity among the damping coefficients of a mass-spring-damper model of a shear building frame. These numerical studies demonstrate the robustness and efficiency of NSBL in alleviating overfitting during Bayesian inversion of nonlinear physics-based models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A study of shock initiation experiments for the explosive PBX 9502 using three reactive burn models

Shock to detonation transition (SDT) experiments are essential in calibrating and validating reactive burn models for explosives. This work investigates the large collection of SDT test data for the explosive PBX 9502 at ambient temperature that was presented by Gustavsen, Sheffield, and Alcon [Journal of Applied Physics, 99, 114907 (2006)]. We first analyze the experimental data and compare two different methods of determining the shock transition time/distance (namely, the bilinear method and the single-curve method). This reveals some of the uncertainty in estimating shock transition points, which contributes to scatter in Pop-plot data. Next, we compare the WSD, AWSD, and SURFplus reactive burn models for a collection of approximately 20 experimental shots using the FLAG hydrocode. Error estimates are used to quantify how well each reactive burn model (and their respective parameter calibrations) performs at predicting the SDT process for a range of loading conditions. Additionally, the importance of mesh resolution and numerical dissipation in SDT simulations will be assessed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Measurement of the 175 Hf half-life

Hafnium-175 is a useful radioisotope for numerous applications; however, its evaluated half-life (70 ± 2 days) has a large uncertainty. To enable a new measurement of the half-life, 175 Hf was produced via proton irradiation of natural lutetium and chemically purified. The 175 Hf sample was counted approximately once a month with three high-purity germanium detectors for 13 months (~5.5 half-lives). A 133 Ba standard was counted in an identical manner to quantify systematic uncertainties over the measurement period. In conclusion, the measured 175 Hf half-life is 69.90 ± 0.07 days, in agreement with the evaluated value, but with significantly reduced uncertainty.

150 ≤ A ≤ 189↗
DOE OSTI2025

Subtropical Jet Regulates Arabian Winter Precipitation: A Viable Mechanism

The present study explores the mechanism governing wintertime (November–April) precipitation over the Arabian Peninsula (AP) using a 17-yr-long (2002–18) high-resolution WRF simulation. The composite analysis of strong precipitation events suggests that the equatorward extension of the upper-level jet together with the embedded upper-level trough creates a positive (cyclonic) midlevel vorticity and subsequently generates an anomalous lower-level convergence through Ekman pumping. This leads to the development of an anomalous surface low, which is further enhanced in the presence of the existing Red Sea trough over the AP. This surface low weakens the persistent anticyclone over the AP, shifting it further eastward to the Arabian Sea. The eastward shift in the lower-level anticyclone contributes to the transport of warm, moist air from the Arabian Sea and the Red Sea toward the AP. This warm, moist air converges with the cold and dry air advected by the midlatitude jet and creates a moisture convergence zone, leading to the initiation of convection. We test the proposed mechanism through numerical experiments with modified upper-level wind and demonstrate that a strong, southward intrusion of the jet can indeed lead to precipitation over the AP. The above mechanism also explains the interannual variability of precipitation over the AP. During wet years, we notice approximately 3 m s -1 stronger jet core magnitude and about a 2° equatorward shift of the jet compared to dry years. While the equatorward extension of the jet explains about 21% of the interannual variability, the jet magnitude explains around 7% of the variability during wet years.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Leverage Score Sampling for Parametric PDEs (Final Technical Report)

This final technical report summarizes the accomplishments of work performed under DOE Office of Science Award DE-SC0022266, which is titled “Leverage Score Sampling for Parametric PDEs”. The goal of the project was to extend methods from Randomized Numerical Linear Algebra (RandNLA) to tackle central computational challenges in model order reduction and uncertainty quantification (UQ) for parametric partial differential equations (PDEs). In particular, we sought to use importance sampling methods originally developed for RandNLA to develop sample efficient active learning algorithms for approximating high-dimensional scalar functions, e.g. by polynomials, Gaussian process models, and simple neural networks. Such methods can be immediately applied to developing surrogate models or to approximating quantity of interest (QoI) surfaces. In the context of PDEs, each sample used for learning equates to the solution of the differential equation for a particular set of parameters, so sample efficiency translates to improved computational efficiency for a variety of downstream tasks.

97 MATHEMATICS AND COMPUTING↗