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At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code. This manuscript serves as a single manual for two separate codes: VARI3D and PERSENT. The VARI3D code (VARIational 3D) is based upon the classic finite difference diffusion theory solver available in DIF3D. The PERSENT code (PERturbation and SENitivity for Transport) is based upon the variational nodal method employed in DIF3D termed VARIANT. The VARIANT solver was added to DIF3D in 1995 and has seen continued development and use for the last 18 years. Because VARI3D primarily uses deprecated coding practices, rather than incorporating the perturbation and sensitivity treatments for transport within VARI3D, a new coding development was built using modern Fortran coding. The primary purpose of this manual is to describe the theory behind PERSENT (and by convenience, that of VARI3D) and discuss the input and output of PERSENT along with giving potential users an idea of how to use it. While this manuscript does describe the input and output of VARI3D, the PERSENT code is intended to be the replacement capability of VARI3D as PERSENT can generate nearly identical (if not superior) diffusion theory results. In this manuscript, the relevant aspects of generalized perturbation theory and exact perturbation theory that apply to both VARI3D and PERSENT are covered. The input and output of VARI3D is displayed by excerpting several of the example problems. Similarly, the input and output of PERSENT is displayed along with tips on how best to use the code. Note that the input and output of the inhomogeneous solver wrapped around DIF3D (DIF3D_IFS) is also discussed as it is needed to carry out some of the sensitivities in PERSENT such as reaction rate ratios. This manuscript describes several perturbation and sensitivity problems, and the results computed using PERSENT. From these sections, potential users should find that PERSENT provides not only the typical tables of numbers desired in perturbation and sensitivity analysis work, but also can visually plot the result for a more thorough understanding of the space and energy distribution (Section 5). Overall, PERSENT is observed to produce accurate reactivity worths and sensitivities for the displayed set of test problems and clearly demonstrates the need to have a transport-based sensitivity capability as evident from the thousands of percent errors observed in the 21-group hexagonal fast reactor problem (covered in Section 7). The uncertainty calculation capability is described in Section 3 and demonstrated in Section 7.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1993

Radiative interactions in molecular gases under local and nonlocal thermodynamic equilibrium conditions

Basic formulations, analyses, and numerical procedures are presented to investigate radiative heat interactions in diatomic and polyatomic gases under local and nonlocal thermodynamic equilibrium conditions. Essential governing equations are presented for both gray and nongray gases. Information is provided on absorption models, relaxation times, and transfer equations. Radiative flux equations are developed which are applicable under local and nonlocal thermodynamic equilibrium conditions. The problem is solved for fully developed laminar incompressible flows between two parallel plates under the boundary condition of a uniform surface heat flux. For specific applications, three diatomic and three polyatomic gases are considered. The results are obtained numerically by employing the method of variation of parameters. The results are compared under local and nonlocal thermodynamic equilibrium conditions at different temperature and pressure conditions. Both gray and nongray studies are conducted extensively for all molecular gases considered. The particular gases selected for this investigation are CO, NO, OH, CO2, H2O, and CH4. The temperature and pressure range considered are 300-2000 K and 0.1-10 atmosphere, respectively. In general, results demonstrate that the gray gas approximation overestimates the effect of radiative interaction for all conditions. The conditions of NLTE, however, result in underestimation of radiative interactions. The method developed for this study can be extended to solve complex problems of radiative heat transfer involving nonequilibrium phenomena.

Tiwari, S. N.↗
NASA NTRS2008

Variations of Strahl Properties with Fast and Slow Solar Wind

The interplanetary solar wind electron velocity distribution function generally shows three different populations. Two of the components, the core and halo, have been the most intensively analyzed and modeled populations using different theoretical models. The third component, the strahl, is usually seen at higher energies, is confined in pitch-angle, is highly field-aligned and skew. This population has been more difficult to identify and to model in the solar wind. In this work we make use of the high angular, energy and time resolution and three-dimensional data of the Cluster/PEACE electron spectrometer to identify and analyze this component in the ambient solar wind during high and slow speed solar wind. The moment density and fluid velocity have been computed by a semi-numerical integration method. The variations of solar wind density and drift velocity with the general build solar wind speed could provide some insight into the source, origin, and evolution of the strahl.

Figueroa-Vinas, Adolfo↗
DOE OSTI2020

Calculations of anisotropic magnetic properties using spin-orbit energy variations

We analyze several methods of obtaining the accurate relativistic total energy (TE) variations using traditional perturbation theories (PTs) and proposed coupling constant integration (CCI) methods. For this purpose, we perform benchmark calculations within the density functional theory taking the spin-orbit coupling (SOC) and its derivative as a perturbation. The TE change due to SOC addition obtained from both PTs and CCI is shown to reach the accuracy of fully self-consistent TE calculations. Similar accuracy is also obtained even for the magnetocrystalline anisotropy energy (MAE). The real advantage of the proposed methods is to use PTs and CCI methods in those electronic structure methods where accurate total energies currently cannot be obtained with required accuracy. Correspondingly, we demonstrate the applicability of suggested methods for calculations of MAE in different magnetic materials using a dynamic mean-field method. All suggested PTs and CCI methods also provide convenient site, orbital, and spin decompositions of the TE variation, creating a powerful way to analyze microscopic physics in strongly correlated materials.

36 MATERIALS SCIENCE↗
NASA NTRS1975

Sasaki's variational optimization analysis of temperature and moisture advection in a severe storm environment

Temperature and moisture advection patterns of dry air intrusion were analyzed by a variational optimization method to relate mesoscale advection to a severe thunderstorm environment. The analysis results presented here were obtained from a case study, May 26, 1973, when a tornado squall line developed in Oklahoma in conjunction with a clearly delineated dry air intrusion. Observations from the synoptic upper air network were used for inputs of horizontal wind components, potential temperature, and mixing ratio at each 50 mb increment from 950 to 100 mb. An objective analysis was performed to assign values of the variables to grid points of a 15 x 14 horizontal grid with approximate 125 km grid spacing at each pressure level. After the analysis the data fields were smoothed using a variational formalism.

Mcfarland, M. J.↗
NASA NTRS1991

Elimination of secular terms from the differential equations for the elements of perturbed two-body motion

In 1961, Sperling linearized and regularized the differential equations of motion of the two-body problem by changing the independent variable from time to fictitious time by Sundman's transformation (r = dt/ds) and by embedding the two-body energy integral and the Laplace vector. In 1968, Burdet developed a perturbation theory which was uniformly valid for all types of orbits using a variation of parameters approach on the elements which appeared in Sperling's equations for the two-body solution. In 1973, Bond and Hanssen improved Burdet's set of differential equations by embedding the total energy (which is a constant when the potential function is explicitly dependent upon time.) The Jacobian constant was used as an element to replace the total energy in a reformulation of the differential equations of motion. In the process, another element which is proportional to a component of the angular momentum was introduced. Recently trajectories computed during numerical studies of atmospheric entry from circular orbits and low thrust beginning in near-circular orbits exhibited numerical instability when solved by the method of Bond and Gottlieb (1989) for long time intervals. It was found that this instability was due to secular terms which appear on the righthand sides of the differential equations of some of the elements. In this paper, this instability is removed by the introduction of another vector integral called the delta integral (which replaces the Laplace Vector) and another scalar integral which removes the secular terms. The introduction of these integrals requires a new derivation of the differential equations for most of the elements. For this rederivation, the Lagrange method of variation of parameters is used, making the development more concise. Numerical examples of this improvement are presented.

Bond, Victor R.↗
DOE OSTI2023

Variational Neural-Network Ansatz for Continuum Quantum Field Theory

Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In nonrelativistic quantum field theories, the challenge is to parametrize and optimize over the infinitely many n-particle wave functions comprising the state’s Fock-space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to nonrelativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parametrize all of the n-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Mapping variations of redshift distributions with probability integral transforms

We present a method for mapping variations between probability distribution functions and apply this method within the context of measuring galaxy redshift distributions from imaging survey data. This method, which we name PITPZ for the probability integral transformations it relies on, uses a difference in curves between distribution functions in an ensemble as a transformation to apply to another distribution function, thus transferring the variation in the ensemble to the latter distribution function. This procedure is broadly applicable to the problem of uncertainty propagation. In the context of redshift distributions, for example, the uncertainty contribution due to certain effects can be studied effectively only in simulations, thus necessitating a transfer of variation measured in simulations to the redshift distributions measured from data. We illustrate the use of PITPZ by using the method to propagate photometric calibration uncertainty to redshift distributions of the Dark Energy Survey Year 3 weak lensing source galaxies. For this test case, we find that PITPZ yields a lensing amplitude uncertainty estimate due to photometric calibration error within 1 per cent of the truth, compared to as much as a 30 per cent underestimate when using traditional methods.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

A machine learning-based interaction force model for non-spherical and irregular particles in low Reynolds number incompressible flows

In this study, interaction force of non-spherical particles in low Reynolds number gas-solid flow is investigated by neural network approaches. An artificial neural network (ANN) model is developed to correlate the non-spherical particle shape and the flow conditions with the interaction force. To define the particle shape, spherical harmonic expansion is applied. Furthermore, variational autoencoder model is then used to extract latent geometric features. The latent vector is utilized as an input with the Reynolds number for the ANN. The interaction force data, which is used as output data of the ANN, is obtained by particle resolved direct numerical simulation for 5200 non-spherical particles. The proposed model enables unsupervised extraction for non-spherical particle shapes and accurate predictions on the interaction force without heavy computation. This study provides the model that can explain complicated shapes of particles and be applied to a large scale, computational fluid dynamics simulation.

01 COAL, LIGNITE, AND PEAT↗
NASA NTRSDate not supplied

Oxygen Isotopic Composition of Refractory Inclusions from the Miller Range (MIL) 090019 Carbonaceous Chondrite

Introduction: Primitive meteorites contain Calcium-Aluminum-rich Inclusions (CAIs)that preserve the records of the earliest times in the Solar System. CAIs record O isotopic variations with time and/or location from solar (16O-rich) to planetary (16O-poor) compositions [e.g., 1, 2].However, CAIs were also affected by parent body processing to varying degrees. The goal of this work was to identify the processes that resulted in the fine-scale spatial variations in oxygen isotopic compositions within the most ancient Solar System solids. We report oxygen isotopic composition of CAIs from MIL 090019 CO3.1 carbonaceous chondrite. MIL 090019 contains a high abundance of CAIs showing mineralogical as well as textural variations [3]. Methods: We analyzed 10 CAIs with different mineralogical assemblages, classified as corundum-bearing, grossite-bearing, hibonite-bearing, melilite-bearing, anorthite-bearing inclusions and amoeboid olivine aggregates(AOA’s). The mineralogical and petrological characterization of CAIs was performed using the JOEL Hyperprobe 8530 electron microprobe at NASA JSC. Oxygen isotopic imaging of the CAIs was done using the Cameca NanoSIMS 50L ion microprobe at NASA JSC. We followed the analytical protocol described in [4]. O-isotopic maps of the CAI were acquired by rastering a ~3 pA primary Cs+beam at 16 keVover an area of 20 ×20μm2over a period of ~7 hours. Negative secondary ions of 16O−, 17O−, 18O−, 28Si−, 24Mg16O−, 27Al16O−, and 40Ca16O−were simultaneously acquired using electron multiplier detectors at a mass resolving power sufficient to resolve the 16OH−interference from the 17O−peak, where the contribution of 16OH−was <0.1%.An electron flood gun was used to mitigate sample charging during the analyses. We used San Carlos olivine and Madagascar hibonite as isotopic standards to correct for the instrumental mass fractionation. The O-isotopic ratios were corrected for the quasi simultaneous arrival (QSA) effect and the detector dead time. All reported errors are 1 sigma. Results: The MIL 090019 carbonaceous chondrite hosts refractory inclusions varying in their mineralogies and textures[2, 3]. We found the oxygen isotopic compositions of mineral phases in MIL 090019 CAIs show large variations with Δ17O values varying from -27 to 0‰. A corundum-bearing inclusion records isotopic variations with corundum, melilite, perovskite, and anorthite showing Δ17Ovalues of -20 ±2.5, -10.2 ± 6.5, -10.7 ± 1.3,and -1.2 ± 3.2‰ respectively. A grossite-hibonite-bearing inclusion also records O-isotopic heterogeneity, where grossite, hibonite, Mg-rich spinel, and melilite show -3.7 ± 2.7, -22.9 ± 2.5, -21.4 ± 2.6, and -17.3 ± 2.8‰ respectively, whereas perovskite grains record a heterogenous isotopic composition ranging from -22.6 to -13.9‰. A hibonite-bearing inclusion shows average Δ17Ο values of -17.6 ± 5.3 ‰ and -15.1 ± 4.8 ‰ for hibonite and spinel respectively. The two perovskite grains also show relatively 16O-poor composition (Δ17Ο = -11.8 ± 6.4 ‰ and -8.6 ± 5.2 ‰). Anorthite has ~0.1 wt% Na2O and ~0.52 wt% FeO and a Δ17Ο value of -7.2 ± 5.0 ‰, whereas diopside records a Δ17Ο value of -3.5 ± 5.0 ‰. A hibonite-spinel-rich inclusion contains spinel and hibonite that are16O-rich (Δ17Οvalues -21.3 ± 2.8‰ and -19.4 ± 3.0‰, respectively). Melilite shows heterogenous oxygen isotopic composition, with an inner 16O-rich region and an outer 16O-poor region separated by a sharp boundary, with a bulk Δ17Ο= -16.2 ± 2.1‰, whereas two perovskite grains are relatively 16O-poor (Δ17Ο= -13.2 ± 3.7‰ and -7.1 ± 3.4‰).A spinel-rich inclusion contains perovskite grains with Δ17Οranging from -27.0 to -22.8 ‰and spinel with average Δ17Οvalue of -21.4 ± 2.8 ‰. In a melilite and spinel-rich CAI, perovskite, spinel, diopside, melilite, and Al-Ti-rich pyroxene record Δ17Ο values of-26.9 ± 4.6‰, -22.4 ± 4.3‰,-23.4 ± 4.9, -19.3 ± 3.4, and -19.0 ± 4.3 ‰ respectively. Olivine and spinel components of 2 AOA’s record a 16O-rich composition with Δ17O~-23‰. Discussion: The coexistence of 16O-rich and 16O-poor minerals within CAIs has been attributed to differing degrees of O isotopic exchange, reflecting a wide range of O diffusion rates[5]. However, the O isotopic heterogeneity observed in these CAIs cannot be explained by oxygen diffusion in nebular or parent body settings alone. The isotopic imaging of CAIs from the MIL 090019 meteorite shows variations in the O isotopic composition recorded in their mineral components, suggesting that these CAIs record the oxygen isotopic heterogeneity in the nebular gas from which they condensed. The coexistence of 16O-rich and 16O-poor mineral components in the CAI-forming region suggests that the gas in this region was not well-mixed and consisted of distinct 16O-rich and 16O-poor gaseous reservoirs.

P Mane↗
DOE OSTI2023

Variational quantum simulation of the critical Ising model with symmetry averaging

Here we investigate the use of deep multiscale entanglement renormalization ansatz (DMERA) circuits as a variational ansatz. We use the exactly solvable one-dimensional critical transverse-field Ising model as a test bed. Numerically exact simulation of the quantum circuit ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, the DMERA strongly outperforms a standard quantum approximate optimization algorithm (QAOA)–style ansatz, and that a major source of systematic error in correlation functions approximated using the DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. Here, we propose that this technique for mitigating systematic error could be applied to noisy intermediate-scale quantum (NISQ) simulations of physical systems with other symmetries.

1-dimensional spin chains↗
DOE OSTI2024

Real-time dynamics of the Schwinger model as an open quantum system with Neural Density Operators

Ab-initio simulations of multiple heavy quarks propagating in a Quark-Gluon Plasma are computationally difficult to perform due to the large dimension of the space of density matrices. This work develops machine learning algorithms to overcome this difficulty by approximating exact quantum states with neural network parametrisations, specifically Neural Density Operators. As a proof of principle demonstration in a QCD-like theory, the approach is applied to solve the Lindblad master equation in the 1 + 1d lattice Schwinger Model as an open quantum system. Neural Density Operators enable the study of in-medium dynamics on large lattice volumes, where multiple-string interactions and their effects on string-breaking and recombination phenomena can be studied. Thermal properties of the system at equilibrium can also be probed with these methods by variationally constructing the steady state of the Lindblad master equation. Scaling of this approach with system size is studied, and numerical demonstrations on up to 32 spatial lattice sites and with up to 3 interacting strings are performed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Helicity, spin, and infra-zilch of light: A Lorentz covariant formulation

Highlights: • Spin and orbital parts of angular momentum. • The helicity tensor contains the helicity, spin and infra-zilch currents. • The helicity tensor is a Noether current for a duality-symmetric action. • Symmetry generator for the helicity tensor. • The helicity tensor is conserved in Lorenz gauge. In this paper, a novel conserved Lorentz covariant tensor, termed the helicity tensor, is introduced in Maxwell theory. The conservation of the helicity tensor expresses the conservation laws contained in the helicity array, introduced by Cameron et al. (2012), including helicity, spin, as well as the spin-flux or infra-zilch. The Lorentz covariance of the helicity tensor is in contrast to previous formulations of the helicity hierarchy of conservation laws, which required the non-Lorentz covariant transverse gauge. The helicity tensor is shown to arise as a Noether current for a variational symmetry of a duality-symmetric Lagrangian for Maxwell theory. This symmetry transformation generalizes the duality symmetry and includes the symmetry underlying the conservation of the spin part of the angular momentum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Attaining regularization length insensitivity in phase-field models of ductile failure

In this work, a cohesive phase-field model of ductile fracture in a finite-deformation setting is presented. The model is based on a free-energy function in which both elastic and plastic work contributions are coupled to damage. Using a strictly variational framework, the field evolution equations, damage kinetics, and flow rule are jointly derived from a scalar least-action principle. Particular emphasis is placed on the use of a rational function for the stress degradation that maintains a fixed effective strength with decreasing regularization length. The model is employed to examine crack growth in pure mode-I problems through the generation of crack growth resistance (J-R) curves. In contrast to alternative models, the current formulation gives rise to J-R curves that are insensitive to the regularization length. Numerical evidence suggests convergence of local fields with respect to diminishing regularization length as well.

42 ENGINEERING↗
DOE OSTI2024

Scalable semidefinite programming approach to variational embedding for quantum many-body problems

In quantum embedding theories, a quantum many-body system is divided into localized clusters of sites which are treated with an accurate ‘high-level’ theory and glued together self-consistently by a less accurate ‘low-level’ theory at the global scale. The recently introduced variational embedding approach for quantum many-body problems combines the insights of semidefinite relaxation and quantum embedding theory to provide a lower bound on the ground-state energy that improves as the cluster size is increased. The variational embedding method is formulated as a semidefinite program (SDP), which can suffer from poor computational scaling when treated with black-box solvers. Here, we exploit the interpretation of this SDP as an embedding method to develop an algorithm which alternates parallelizable local updates of the high-level quantities with updates that enforce the low-level global constraints. Moreover, we show how translation invariance in lattice systems can be exploited to reduce the complexity of projecting a key matrix to the positive semidefinite cone.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Noether currents for Eulerian variational principles in non-barotropic magnetohydrodynamics and topological conservations laws

We derive a Noether current for the Eulerian variational principle of ideal non-barotropic magnetohydrodynamics (MHD). It was shown previously that ideal non-barotropic MHD is mathematically equivalent to a five function field theory with an induced geometrical structure in the case that field lines cover surfaces and this theory can be described using a variational principle. Here we use various symmetries of the flow to derive topological constants of motion through the derived Noether current and discuss their implication for non-barotropic MHD.

42 ENGINEERING↗
DOE OSTI2020

Cross-Sections of Nanocellulose from Wood Analyzed by Quantized Polydispersity of Elementary Microfibrils

Bio-based nanocellulose has been shown to possess impressive mechanical properties and simplicity for chemical modifications. The chemical properties are largely influenced by the surface area and functionality of the nanoscale materials. However, finding the typical cross-sections of nanocellulose, such as cellulose nanofibers (CNFs), has been a long-standing puzzle, where subtle changes in extraction methods seem to yield different shapes and dimensions. Here, we extracted CNFs from wood with two different oxidation methods and variations in degree of oxidation and high-pressure homogenization. Additionally, the cross-sections of CNFs were characterized by small-angle X-ray scattering and wide-angle X-ray diffraction in dispersed and freeze-dried states, respectively, where the results were analyzed by assuming that the cross-sectional distribution was quantized with an 18-chain elementary microfibril, the building block of the cell wall. We find that the results agree well with a pseudosquare unit having a size of about 2.4 nm regardless of sample, while the aggregate level strongly depends on the extraction conditions. Furthermore, we find that aggregates have a preferred cohesion of phase boundaries parallel to the (110)-plane of the cellulose fibril, leading to a ribbon shape on average.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Emulation With Uncertainty Quantification of Regional Sea‐Level Change Caused by the Antarctic Ice Sheet

Abstract Projecting regional sea‐level change under various climate‐change scenarios typically involves running forward simulations of the Earth's gravitational, rotational and deformational (GRD) response to ice‐mass change, which requires substantial computational cost if applied to probabilistic frameworks requiring thousands to millions of samples. Here we build emulators of regional sea‐level change at 27 coastal locations, due to the GRD effects associated with future Antarctic Ice Sheet mass change over the 21st century. The emulators are evaluated against a numerical sea‐level model applied to an ensemble of ice‐sheet model simulations of the Antarctic Ice Sheet through 2100. We build a physics‐based emulator using a recent sensitivity kernel approach and compare it to machine learning based emulators (neural network and conditional variational autoencoder methods). In order to quantify uncertainty, we derive well‐calibrated prediction intervals for regional sea‐level change via split‐conformal inference and linear regression, and show that Monte Carlo dropout does not yield well‐calibrated uncertainties in this instance. We also demonstrate substantial gains in computational efficiency using both the physics‐based emulator and neural networks in comparison to the numerical model for the complete regional sea‐level solution. Overall, we find the physics‐based emulator modestly outperforms the machine learning emulators for this problem.

58 GEOSCIENCES↗