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At least 325 records · Page 18

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DOE OSTI2021

Tensor network study of the m = 1/2 magnetization plateau in the Shastry-Sutherland model at finite temperature

The two-dimensional infinite projected entangled pair state tensor network is evolved in imaginary time with the full update (FU) algorithm to simulate the Shastry-Sutherland model in a magnetic field at finite temperature directly in the thermodynamic limit. We focus on the phase transition into the m = 1/2 magnetization plateau, which was observed in experiments on SrCu 2 (BO 3 ) 2 . For the largest simulated bond dimension, the early evolution in the high-temperature regime is simulated with the simple update (SU) scheme and then, as the correlation length increases, continued with the FU scheme towards the critical regime. We apply a small symmetry-breaking bias field and then extrapolate towards zero bias using a simple scaling theory in the bias field. The combined SU + FU scheme provides an accurate estimate of the critical temperature, even though the results could not be fully converged in the bond dimension in the vicinity of the transition. Here, the critical temperature estimate is improved with a generalized scaling theory that combines two divergent length scales: One due to the bias, and the other due to the finite bond dimension. The obtained results are consistent with the transition being in the universality class of the two-dimensional classical Ising model. The estimated critical temperature is 3.5(2) K, which is well above the temperature 2.1 K used in the experiments.

2-dimensional systems↗

DOE OSTI2021

Seismic source characterization of the Arabian Peninsula and Zagros Mountains from regional moment tensor and coda envelopes

Reliable estimates of moment magnitude and source mechanism for seismic events in the Middle East can be challenging due to a small number of openly available stations, the complex tectonic setting, and regions of high attenuation. Access to high-quality waveform data from well-calibrated regional seismic stations is fundamental in producing robust and stable estimates of earthquake source parameters, particularly when measurements of absolute ground motion amplitudes are required. Earthquake source mechanism and moment magnitude are invaluable information in the assessment of seismic hazard, plate motions, and the characterization of faults and regional stress field. The expansion of the Kingdom of Saudi Arabia’s national seismic network in the past several decades provides an opportunity to develop the capabilities of routine focal mechanism and moment magnitude estimations. In this study, we use time-domain full waveform moment tensor inversion and coda envelope–derived amplitude measurements to solve for earthquake source mechanism, moment magnitudes, and their source type. Furthermore, we compared the moment magnitudes calculated from the two methods and publicly available earthquake catalogs and discuss the implications of the obtained source parameters.

58 GEOSCIENCES↗

DOE OSTI2022

General tensor structure for electron scattering in terms of invariant responses

The general structure of semi-inclusive polarized electron scattering from polarized spin-1/2 targets is developed for use at all energy scales, from modest-energy nuclear physics applications to use in very high energy particle physics. The leptonic and hadronic tensors that enter in the formalism are constructed in a general covariant way in terms of kinematic factors that are frame dependent but model independent and invariant response functions which contain all of the model-dependent dynamics. In the process of developing the general problem the relationships to the conventional responses expressed in terms of the helicity components of the exchanged virtual photon are presented. For semi-inclusive electron scattering with polarized electrons and polarized spin-1/2 targets one finds that 18 invariant response functions are required, each depending on four Lorentz scalar invariants. Additionally it is shown how the semi-inclusive cross sections are related via integrations over the momentum of the selected coincidence particle and sums over open channels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

GPU-acceleration of tensor renormalization with PyTorch using CUDA

We show that numerical computations based on tensor renormalization group (TRG) methods can be significantly accelerated with PyTorch on graphics processing units (GPUs) by leveraging NVIDIA's Compute Unified Device Architecture (CUDA). Here we find improvement in the runtime and its scaling with bond dimension for two-dimensional systems. Our results establish that the utilization of GPU resources is essential for future precision computations with TRG.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Thermophysical properties of FLiBe using moment tensor potentials

Fluoride salts are prospective materials for applications in some next-generation nuclear reactors and their thermophysical properties at various conditions are of interest. Experimental measurement of the properties of these salts is often difficult and, in some cases, unfeasible due to challenges from high temperatures, impurity control, and corrosivity. Therefore, accurate theoretical methods are needed for fluoride salt property prediction. In this work, we used moment tensor potentials (MTP) to approximate the potential energy surface of eutectic FLiBe (66.6% LiF – 33.3% BeF2) predicted by the ab initio (DFT-D3) method. Here, we then used the developed potential and molecular dynamics to obtain several thermophysical properties of FLiBe, including radial distribution functions, density, self-diffusion coefficients, thermal expansion, specific heat capacity, bulk modulus, viscosity, and thermal conductivity. Our results show that the MTP potential approximates the potential energy surface accurately and the overall approach yields very good agreement with experimental values. The converged fitting can be obtained with less than 600 configurations generated from DFT calculations, which data can be generated in just 1200 core hours on today's typical processors. The MTP potential is faster than many machine learning potentials and about one order of magnitude slower than widely used empirical molten salt potentials such as Tosi/Fumi.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Tensor-polarized parton density in the $N → Δ$ transition

The generalized parton distributions for transitions between baryon states with different masses have a forward limit in which they behave as parton densities (light-front momentum transfer Δ + , Δ T = 0, energy transfer Δ - ≠ 0). These "transition parton densities" can realize spin/isospin quantum numbers not accessible in the ground-state nucleon. The N → Δ transition gives rise to a new parton density proportional to the 1/2 → 3/2 spin transition tensor. Its properties are derived, and its magnitude is estimated in the chiral quark-soliton model based on the large-N c limit of QCD.

Delta isobar↗

DOE OSTI2021

Regional Moment Tensor Inversion Using Rotational Observations

There are benefits from the addition of rotational motions to translational displacements for moment tensor (MT) inversions. The rotational radiation pattern is orthogonal to the shear radiation pattern, thus incorporating rotations is equivalent to gaining another observation point on the focal sphere. We demonstrated this by simulating curl and displacement wavefields for a regional distance station. Thus, one 6-C station (3-Component translational + 3-Component rotational) gathers the same information on radiation pattern as two 3-C stations at 90° azimuth from one another along the focal plane axis, which is sometimes difficult to obtain when restricted to surface sensors. We added rotational Green's functions to a regional MT inversion scheme (long-period, time-domain, and linear inversion) by computing spatial gradients from f-κ reflectivity synthetics. For rotational data, we used Array Derived Rotations (ADR) from Piñon Flats Observatory Array and Golay array deployed during IRIS Community Wavefield Demonstration Experiment. The hope is to ultimately use compact and field deployable broadband rotational seismometers instead of ADRs. Rotational motions were predicted from well-constrained deviatoric MT solutions of nine earthquakes recorded by the arrays and other seismic networks. Additionally, we formed three station sparse datasets with (3-C and 6-C) and without rotational ground motions (3-C only) for eight earthquakes testing the benefits of including rotational waveforms in MT inversions when they are equally weighted with translational waveforms. Adding rotational motions improved the double-couple components and reduced compensated-linear-vector-dipole and isotropic components in full-MT solutions using sparse datasets with poor coverage.

58 GEOSCIENCES↗

DOE OSTI2022

Pairwise connected tensor network representation of path integrals

It has been recently shown how the tensorial nature of real-time path integrals (PIs) involving the Feynman-Vernon influence functional can be utilized with matrix product states, taking advantage of the finite length of the bath-induced memory. Tensor networks (TNs) promise to provide a unified language to express the structure of a PI. A generalized TN specifically incorporating the pairwise interaction structure of the influence functional and its invariance with respect to the average forward-backward position or the sojourn value in the form of the blip representation is derived and implemented. This pairwise connected TNPI (PC-TNPI) is illustrated through applications to typical spin-boson problems and explorations of the differences caused by the exact form of the spectral density. The storage and performance scalings are reported, showing the compactness of the representation and the efficiency of the contraction process. Finally, taking advantage of the compressed representation, the viability of using PC-TNPI for simulating multistate problems is demonstrated. The PC-TNPI structure can be shown to yield other TN algorithms currently in use. Consequently, it should be possible to use it as a starting point for deriving other optimized procedures.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions

The locality of field theories strongly constrains the possible behaviors of symmetry-twisted partition functions, and thus they serve as order parameters to detect low-energy realizations of global symmetries, such as spontaneous symmetry breaking (SSB). We demonstrate that the tensor renormalization group (TRG) offers an efficient framework to compute the symmetry-twisted partition functions, which enables us to detect the symmetry-breaking transition and also to study associated critical phenomena. As concrete examples of SSB, we investigate the two-dimensional (2D) classical Ising model and the three-dimensional (3D) classical 𝑂⁡(2) nonlinear sigma model, and we identify their critical points solely from the twisted partition function. By employing the finite-size scaling argument, we find the critical temperature 𝑇 𝑐 = 2.2017⁢(2) with the critical exponent 𝜈 = 0.663⁢(33) for the 3D 𝑂⁡(2) model. In addition, we also study the Berezinskii–Kosterlitz–Thouless (BKT) criticality of the 2D classical 𝑂⁡(2) model by extracting the helicity modulus from the twisted partition functions, and we obtain the BKT transition temperature, 𝑇 BKT = 0.8928⁢(2).

lattice field theory↗

DOE OSTI2022

Utah FORGE: Phase 1a Tensor Strainmeter Data for the April, 2022 Stimulation of Well 16A(78)-32

Data from two Tensor Optical Fiber Strainmeters that were operational during Stages 1, 2, and 3 of the April, 2022 stimulation of well 16A(78)-32. Each csv file contains data from each stimulation stage (stage1, stage2, stage3) for both Phase 1a strainmeter installations (FS01, formerly FS-C, and FS02, formerly FS1-2) in human-readable comma-separated value text files. There are two header lines in each file describing the data contained in that column along with their units, respectively. Data have been decimated from 2 to 1 Hz to match the Pason data found in the linked GDR dataset below (16A78-32 Stimulation Pason Data). These files contain the time series spanning the same time interval as the Pason data as well as ambient data for 5 hours before the stimulation and 5 hours following shut in. The station locations were chosen based on their proximity to the borehole seismometers owned and operated by the University of Utah. See README.txt for more information.

15 GEOTHERMAL ENERGY↗

DOE OSTI2022

A Hybrid Method for Tensor Decompositions that Leverages Stochastic and Deterministic Optimization

In this paper, we propose a hybrid method that uses stochastic and deterministic search to compute the maximum likelihood estimator of a low-rank count tensor with Poisson loss via state-of-theart local methods. Our approach is inspired by Simulated Annealing for global optimization and allows for fine-grain parameter tuning as well as adaptive updates to algorithm parameters. We present numerical results that indicate our hybrid approach can compute better approximations to the maximum likelihood estimator with less computation than the state-of-the-art methods by themselves.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Transmural Remodeling of Cardiac Microstructure in Aged Spontaneously Hypertensive Rats by Diffusion Tensor MRI

The long-standing high blood pressure (also known as hypertension) overworks the heart. Microstructural remodeling is a key factor of hypertensive heart disease progression. Diffusion tensor magnetic resonance imaging (DT-MRI) is a powerful tool for the rapid noninvasive nondestructive delineation of the cardiomyocyte organization. The spontaneously hypertensive rat (SHR) is a well-established model of genetic hypertension. The goal of this study was to employ high-resolution DT-MRI and the SHR animal model to assess the transmural layer-specific remodeling of myocardial microstructure associated with hypertension. Ex vivo experiments were performed on excised formalin-fixed hearts of aged SHRs (n = 4) and age-matched controls (n = 4). The DT-MRI-derived fractional anisotropy (FA), longitudinal diffusivity (λ L ), transversal diffusivity (λ T ), and mean diffusivity (MD) served as the readout parameters investigated at three transmural zones (i.e., endocardium, mesocardium, and epicardium). The helix angles (HAs) of the aggregated cardiomyocytes and the orientation of laminar sheetlets were also studied. Compared with controls, the SHRs exhibited decreased epicardial FA, while FA changes in the other two transmural regions were insignificant. No substantial differences were observed in the diffusivity parameters and the transmural course of HAs between the two groups. A consistent distribution pattern of laminar sheetlet orientation was not identified for either group. Our findings are in line with the known cellular microstructure from early painstaking histological studies. Biophysical explanations of the study outcomes are provided. In conclusion, our experimental findings indicate that the epicardial microstructure is more vulnerable to high blood pressure leading to more pronounced changes in this region during remodeling. DT-MRI is well-suited for elucidating these alterations. The revealed transmural nonuniformity of myocardial reorganization may shed light on the mechanisms of the microstructure-function relationship in hypertension progression. Our results provide insights into the management of patients with systemic arterial hypertension, thus prevent the progression toward heart failure. The findings of this study should be acknowledged by electromechanical models of the heart that simulate the specific cardiac pathology.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1964