Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Matrix models”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Seasonal Disorder in Urban Traffic Patterns: A Low Rank Analysis

This article proposes several advances to sparse nonnegative matrix factorization (SNMF) as a way to identify large-scale patterns in urban traffic data. The input to our model is traffic counts organized by time and location. Nonnegative matrix factorization additively decomposes this information, organized as a matrix, into a linear sum of temporal signatures. Penalty terms encourage this factorization to concentrate on only a few temporal signatures, with weights which are not too large. Our interest here is to quantify and compare the regularity of traffic behavior, particularly across different broad temporal windows. In addition to the rank and error, we adapt a measure introduced by Hoyer to quantify sparsity in the representation. Combining these, we construct several curves which quantify error as a function of rank (the number of possible signatures) and sparsity; as rank goes up and sparsity goes down, the approximation can be better and the error should decreases. Plots of several such curves corresponding to different time windows leads to a way to compare disorder/order at different time scalewindows. In this paper, we apply our algorithms and procedures to study a taxi traffic dataset from New York City. In this dataset, we find weekly periodicity in the signatures, which allows us an extra framework for identifying outliers as significant deviations from weekly medians. We then apply our seasonal disorder analysis to the New York City traffic data and seasonal (spring, summer, winter, fall) time windows. We do find seasonal differences in traffic order.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Effect of Nucleation Heterogeneity on Mineral Precipitation in Confined Environments

Abstract The formation of new mineral phases in confined environments, especially in porous media, is crucial for various geological processes like mineralization and diagenesis. The nucleation and precipitation of minerals are initiated at the microscale through fluid‐rock interaction, where dissolution of primary phases leads to supersaturated conditions and nucleation and growth of secondary ones. Previous research has focused primarily on either precipitation or nucleation, without fully exploring their combined impact. Our study introduces a computational framework that integrates classical nucleation theory with the micro‐continuum method. We validated our model by comparing with experiments, and discovered that different surface nucleation rate changes the mode of precipitation from a preferential to uniform precipitate textures. Furthermore, our study uncovered that the conventional deterministic precipitation method tends to underestimate the permeability of the porous matrix. In contrast, the new framework significantly improves model accuracy by incorporating preferential precipitation and heterogeneous nucleation.

58 GEOSCIENCES↗
DOE OSTI2021

Approaching the self-dual point of the sinh-Gordon model

One of the most striking but mysterious properties of the sinh-Gordon model (ShG) is the b → 1/b self-duality of its S-matrix, of which there is no trace in its Lagrangian formulation. Here b is the coupling appearing in the model’s eponymous hyperbolic cosine present in its Lagrangian, cosh(bΦ). In this paper we develop truncated spectrum methods (TSMs) for studying the sinh-Gordon model at a finite volume as we vary the coupling constant. We obtain the expected results for b << 1 and intermediate values of b, but as the self-dual point b = 1 is approached, the basic application of the TSM to the ShG breaks down. We find that the TSM gives results with a strong cutoff Ec dependence, which disappears according only to a very slow power law in Ec. Standard renormalization group strategies — whether they be numerical or analytic — also fail to improve upon matters here. We thus explore three strategies to address the basic limitations of the TSM in the vicinity of b = 1. In the first, we focus on the small-volume spectrum. We attempt to understand how much of the physics of the ShG is encoded in the zero mode part of its Hamiltonian, in essence how ‘quantum mechanical’ vs ‘quantum field theoretic’ the problem is. In the second, we identify the divergencies present in perturbation theory and perform their resummation using a supra-Borel approximate. In the third approach, we use the exact form factors of the model to treat the ShG at one value of b as a perturbation of a ShG at a different coupling. In the light of this work, we argue that the strong coupling phase b > 1 of the Lagrangian formulation of model may be different from what is naïvely inferred from its S-matrix. In particular, we present an argument that the theory is massless for b > 1.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Bayesian chain graph models to characterize microbe-environment dynamics

Microbiome data require statistical models that can simultaneously decode microbes' reaction to the environment and interactions among microbes. While a multiresponse linear regression model seems like a straight-forward solution, we argue that treating it as a graphical model is problematic given that the regression coefficient matrix does not encode the conditional dependence structure between response and predictor nodes. This observation is especially important in biological settings when we have prior knowledge on the edges from specific experimental interventions that can only be properly encoded under a conditional dependence model. Here, we propose a chain graph model with two sets of nodes (predictors and responses) whose solution yields a graph with edges that indeed represent conditional dependence, thus agreeing with the experimenter's intuition on the average behavior of nodes under treatment. The solution to our model is sparse via the Bayesian linear regression (LASSO). In addition, we propose an adaptive extension so that different shrinkages can be applied to different edges to incorporate edge-specific prior knowledge. Our model is computationally inexpensive through an efficient Gibbs sampling algorithm and can account for binary, counting, and compositional responses via an appropriate hierarchical structure. We test the performance of our model in a variety of simulated datasets, thereby showing superior performance to state-of-the-art approaches. We further apply our model to human gut and soil microbial compositional datasets, and we highlight that CG-LASSO can estimate biologically meaningful network structures in the data.

compositional data↗
DOE OSTI2022

Ferromagnetism and doublon localization in a Wannier-Hubbard chain

We derive a “Wannier-Hubbard” model consisting of an array of overlapping atomic orbitals interacting via a local Coulomb interaction. Transforming to an orthogonal Wannier basis set, the resulting Hamiltonian displays long-range hopping and interactions, with new terms such as correlated hopping and ferromagnetic direct exchange, among others. We numerically study the one-dimensional version of the model at half-filling using the density matrix renormalization group method, unveiling a rich phase diagram as a function of the interaction U and the overlap s with metallic and ferromagnetic phases separated by a ferrimagnetic region. Our results indicate a path toward understanding emergent phases under pressure and beyond standard model Hamiltonians.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Distributed-Memory Sparse Deep Neural Network Inference Using Global Arrays

Partitioned Global Address Space (PGAS) models exhibit tremendous promise in developing efficient and productive distributed-memory parallel applications. They have been used extensively in scientific computations due to conveniently offering a ``shared-memory''-like model and convenient interfaces that separate communication with synchronization. Traditionally, PGAS communication models have been applied to dense/contiguously distributed data, but most modern applications depict varied levels of sparsity. Existing PGAS models require certain adaptations to support distributed sparse computations, since associated computations often require matrix arithmetic, in addition to data movement. The Global Arrays toolkit from Pacific Northwest National Laboratory (PNNL) is one of the earliest PGAS models to combine one-sided data communication and distributed matrix operations and is still used in the popular NWChem quantum chemistry suite. Recently, we have expanded the Global Arrays toolkit to support common sparse operations, like sparse matrix-dense matrix multiplies (SpMM), sparse matrix-sparse matrix multiplication (SpGEMM) and Sampled Dense-Dense Matrix Multiplication (SDDMM). As it turns out, these operations are the bedrock of sparse Deep Learning (DL); sparse deep neural networks and Graph Neural Networks (GNNs) have gained increasing attention recently in achieving speedups on training and inference with reduced memory footprints. Unlike scientific applications in High Performance Computing (HPC), modern (distributed-memory capable) DL toolkits often rely on non-standardized and closed-source vendor software optimizations, creating challenges in software-hardware co-design at scale. Our goal is to support a variety of distributed-memory sparse matrix operations and helper functions in the newly created Sparse Global Arrays (SGA), such that it is possible to build portable and productive Machine Learning scenarios for algorithm/software and hardware codesign purposes. Contemporary data-parallel schemes for training/inference are undergoing a major overhaul since model replication limits scalability and causes resource inefficiencies. As such, we have adopted tensor parallelism in decomposing the model and inputs, to mitigate memory issues. Current implementation is built on top of MPI and uses CPUs to maximize the portability across the platforms.

Distributed computing, machine learning↗
DOE OSTI2021

Attention-based quantum tomography

Abstract With rapid progress across platforms for quantum systems, the problem of many-body quantum state reconstruction for noisy quantum states becomes an important challenge. There has been a growing interest in approaching the problem of quantum state reconstruction using generative neural network models. Here we propose the ‘attention-based quantum tomography’ (AQT), a quantum state reconstruction using an attention mechanism-based generative network that learns the mixed state density matrix of a noisy quantum state. AQT is based on the model proposed in ‘Attention is all you need’ by Vaswani et al (2017 NIPS ) that is designed to learn long-range correlations in natural language sentences and thereby outperform previous natural language processing (NLP) models. We demonstrate not only that AQT outperforms earlier neural-network-based quantum state reconstruction on identical tasks but that AQT can accurately reconstruct the density matrix associated with a noisy quantum state experimentally realized in an IBMQ quantum computer. We speculate the success of the AQT stems from its ability to model quantum entanglement across the entire quantum system much as the attention model for NLP captures the correlations among words in a sentence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Universal Kardar-Parisi-Zhang Dynamics in Integrable Quantum Systems

Although the Bethe ansatz solution of the spin-1/2 Heisenberg model dates back nearly a century, the anomalous nature of its high-temperature transport dynamics has only recently been uncovered. Indeed, numerical and experimental observations have demonstrated that spin transport in this paradigmatic model falls into the Kardar-Parisi-Zhang (KPZ) universality class. This has inspired the significantly stronger conjecture that KPZ dynamics, in fact, occur in all integrable spin chains with non-Abelian symmetry. Here, in this letter, we provide extensive numerical evidence affirming this conjecture. Moreover, we observe that KPZ transport is even more generic, arising in both supersymmetric and periodically driven models. Motivated by recent advances in the realization of SU(N)-symmetric spin models in alkaline-earth-based optical lattice experiments, we propose and analyze a protocol to directly investigate the KPZ scaling function in such systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Bound states in the B -matrix formalism for the three-body scattering

In this work, we consider a model of relativistic three-body scattering with a bound state in the two-body subchannel. We show that the naiïve K-matrix type parametrization, here referred to as the B-matrix, has nonphysical singularities near the physical region. We show how to eliminate such singularities by using dispersion relations and also show how to reproduce unitarity relations by taking into account all relevant open channels.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Reactive Transport Modeling of Shale–Fluid Interactions after Imbibition of Fracturing Fluids

Injection of hydraulic fracturing fluid (HFF) into shale formations for unconventional oil/gas production results in chemical reactions in the shale matrix. Our recent experimental study determined the depths to which different types of reactions between the shale matrix and the HFF extended. In the present study, we built continuum-scale reactive transport models to understand the coupling of chemical reactions and the transport of aqueous species in these shale–HFF systems. Calibration of the model with our previous experimental results reveals that it takes hours to months for the shale matrix to completely neutralize the imbibed acids, depending primarily upon the carbonate content of the shale. Both the HFF pH and pore pH affect the location of barite precipitation, resulting in unique barite precipitation profiles extending millimeters into calcite-rich Eagle Ford shale but only tens of micrometers into low-carbonate Marcellus shale. In addition, dissolved oxygen and extracted bitumen are key to reproducing the experimental observation of Fe(III) (oxyhydr)oxide formation in the shale matrix as a result of pyrite dissolution in the shales. A comparison between the modeling results of porosity in the present study to experimentally measured permeabilities in our previous study suggests that chemical reactions occurring at a greater depth than the observable reaction zone might have impacted permeability. Our model serves as a benchmark for efficiently modeling water–rock interactions in similar systems where bulk rock samples react with a solution in batch reactors. Important reactive transport processes were ascertained via modeling, which allows for quantitative prediction of shale–HFF interactions in shale matrices given the shale and HFF compositions.

58 GEOSCIENCES↗
DOE OSTI2024

Segmentation of RDX and TNT in X‐Ray Computed Tomography Reconstructions of Melt‐Cast Explosives

ABSTRACT Three‐dimensional mesoscale characterization of heterogeneous melt‐cast high explosives is challenging because of the difficulty differentiating binder from explosive crystals: two functionally different materials which are typically similar in density by design. Here, we report an algorithm which can differentiate hexahydro‐1,3,5‐trinitro‐1,3,5‐triazine (RDX) from 2,4,6‐trinitrotoluene (TNT) in x‐ray computed tomography (CT) volumes with tens of microns resolution. This method allows us to quantify RDX/TNT content, porosity, and RDX domain size. We calibrated the segmentation algorithm using simulated x‐ray CT volumes containing object models of RDX crystals within a TNT matrix. We then segmented and analyzed CT data for Composition B (Comp B), a 60/40 RDX/TNT mixture, and Cyclotol, a 75/25 RDX/TNT mixture. We examined melt‐cast samples fabricated with 100% theoretical maximum density (TMD) and 85% TMD. For the 100% TMD Comp B and Cyclotol samples, the RDX content values calculated by segmentation were 3% and 9% lower, respectively, than the values measured by high‐performance liquid chromatography on material from the same synthesis lots. This result is consistent with the expected underreporting of RDX content resulting from x‐ray CT resolution limits on RDX particles with diameters smaller than 25 µm. The 85% TMD samples were less accurately segmented with our algorithm due to the confounding presence of voids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Density functional theory calculations of the mixing enthalpy of ternary uranium carbide compounds

The high melting point of uranium-zirconium carbides (U,Zr)C makes them an ideal fuel for nuclear thermal propulsion (NTP) reactors. Gaps remain in the current understanding of the U-Zr-C system due to the difficulty of conducting thermodynamic experiments at NTP operation conditions. Density functional theory calculations using the Hubbard U model (DFT+U) were performed using orbital matrix occupation (OMC) to obtain the mixing enthalpy for UC and ZrC for (U,Zr)C ternary compounds. Similarly, DFT+U calculations were also carried out for the (U,Nb)C and (U,Ta)C systems. In conclusion, the DFT results are envisioned to be used in thermodynamic assessments of the uranium carbide systems based on the CALPHAD approach to supplement the lack of experimental data for the mixing thermodynamics.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Matrix Approach to Accelerate Spin-Up of CLM5

Numerical models have been developed to investigate and understand responses of biogeochemical cycle to global changes. Steady state, when a system is in dynamic equilibrium, is generally required to initialize these model simulations. However, the spin-up process that is used to achieve steady state pose a great burden to computational resources, limiting the efficiency of global modeling analysis on biogeochemical cycles. This study introduces a new Semi-Analytical Spin-Up (SASU) to tackle this grand challenge. We applied SASU to Community Land Model version 5 and examined its computational efficiency and accuracy. At the Brazil site, SASU is computationally 7 times more efficient than (or saved up to 86% computational cost in comparison with) the traditional native dynamics (ND) spin-up to reach the same steady state. Globally, SASU is computationally 8 times more efficient than the accelerated decomposition spin-up and 50 times more efficient than ND. In summary, SASU achieves the highest computational efficiency for spin-up on site and globally in comparison with other spin-up methods. It is generalizable to wide biogeochemical models and thus makes computationally costly studies (e.g., parameter perturbation ensemble analysis and data assimilation) possible for a better understanding of biogeochemical cycle under climate change.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Band-mixing effects in one-dimensional charge transfer insulators

The low-energy properties of transition metal oxides (TMOs) are governed by the electrons occupying strongly correlated $d$-orbitals that are hybridized with surrounding ligand oxygen $p$ orbitals to varying degrees. Their physics is thus established by a complex interplay between the transition-metal (TM)-ligand hopping $t$, charge transfer energy $\Delta_\mathrm{CT}$, and on-site TM Hubbard repulsion $U$. Here, we study the spectral properties of a one-dimensional (1D) analog of such a $pd$ system, with alternating TM $d$ and ligand anion $p$ orbitals situated along a chain. Using the density matrix renormalization group method, we study the model's single-particle spectral function, x-ray absorption spectrum, and dynamical spin structure factor as a function of $\Delta_\mathrm{CT}$ and $U$. In particular, we present results spanning from the Mott insulating ($\Delta_\mathrm{CT} > U$) to negative charge transfer regime $\Delta_\mathrm{CT} < 0$ to gain a better understanding of the ground and momentum-resolved excited state properties of these different regimes. Our results can guide new studies on TMOs that seek to situate them within the Mott-Hubbard/charge transfer insulator classification scheme.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Revisiting the three-kaon interaction and its relation with 𝐾⁡(1460)

Here, we test the hypothesis of 𝐾⁡(1460) being a hadronic 𝐽 𝑃 = 0 − molecule through nonperturbative 𝑆-wave $KK\bar{⁢K}$, 𝐾⁢𝜋⁢𝜋, 𝐾⁢𝜋⁢𝜂 coupled-channel dynamics in a three-body unitary isobar approach. The scalar two-body coupled-channel resonances 𝑓 0 ⁡(500), 𝑓 0 ⁡(980), 𝑎 0 ⁡(980), and 𝐾$^*_0$⁡(700) are generated in the subsytems in amplitudes that match phase shifts from experiment. In a first step, previous results in the limit of mass-degenerate, stable 𝑓 0 and 𝑎 0 isobars are reproduced. Once the full seven-coupled channel model is switched on, other 𝑆-matrix effects obscure and modify the resonance signal, including complex thresholds, a two-body cusp, and a triangle singularity at threshold.

Döring, M. [George Washington Univ., Washington, D↗