Search NASA⌕ Search

SEARCH · Search NASA

Results for “random fields”

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 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

INTERSTELLAR PICKUP ION ACCELERATION IN THE TURBULENT MAGNETIC FIELD AT THE SOLAR WIND TERMINATION SHOCK USING A FOCUSED TRANSPORT APPROACH

We study the physics of locally born interstellar pickup proton acceleration at the nearly perpendicular solar wind termination shock (SWTS) in the presence of a random magnetic field spiral angle using a focused transport model. Guided by Voyager 2 observations, the spiral angle is modeled with a q -Gaussian distribution. The spiral angle fluctuations, which are used to generate the perpendicular diffusion of pickup protons across the SWTS, play a key role in enabling efficient injection and rapid diffusive shock acceleration (DSA) when these particles follow field lines. Our simulations suggest that variation of both the shape ( q -value) and the standard deviation ( σ -value) of the q -Gaussian distribution significantly affect the injection speed, pitch-angle anisotropy, radial distribution, and the efficiency of the DSA of pickup protons at the SWTS. For example, increasing q and especially reducing σ enhances the DSA rate.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Influence of the pulsating electric field on the ECR heating in a nonuniform magnetic field

According to a computer simulation, the randomized pulsating electric field can strongly influence the ECR plasma heating in a nonuniform magnetic field. It has been found out that the electron energy spectrum is shifted to the high energy region. The obtained effect is intended to be used in the ECR sources for effective X-ray generation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Emergent Gauge Fields from Curvature in Single Layers of Transition-Metal Dichalcogenides

We analyze the electron dynamics in corrugated layers of transition-metal dichalcogenides. Due to the strong spin-orbit coupling, the intrinsic (Gaussian) curvature leads to an emergent gauge field associated with the Berry connection of the spinor wave function. We discuss the gauge field created by topological defects of the lattice, namely, tetragonal and octogonal disclinations and edge dislocations. Ripples and topological disorder induce the same dephasing effects as a random magnetic field, suppressing the weak localization effects. This geometric magnetic field can be detected in an Aharonov-Bohm interferometry experiment by measuring the local density of states in the vicinity of corrugations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Measuring representative volume elements from high-resolution grain-scale strain fields

Most crystalline materials present a highly heterogeneous response at the microscale, which can be affected by both internal factors (such as microstructural parameters) and external factors (such as loading). Relating microscale inhomogeneities to the macroscale response of a material requires the use of homogenisation techniques, usually based on the concept of a representative volume element (RVE)—the smallest volume of material that represents the global average response. Here, in this work, we present a new and robust experimental method of measuring the size of a strain-based RVE from high-resolution grain-scale strain fields obtained using digital image correlation (DIC). The proposed method is based on the statistical (stereological) nature of the RVE, which has been widely adopted in numerical studies, and involves dividing a strain field into randomly selected regions of varying sizes and statistically analysing the distributions of average strains within them. To validate the new method, we generate a large number of synthetic strain fields from a fractional Gaussian noise algorithm. The proposed stereological method is shown to be capable of producing reliable RVE measurements from a very large range of possible microscale strain fields while at the same time being robust in that it can produce RVE measurement results even in cases where other existing methods may be unable to do so. The proposed method has a low field-of-view requirement, only needing a field-of-view about 1.2 times as large as the RVE to produce reliable measurements. In addition, the stereological method offers significant flexibility since its statistical nature allows for control over how strict the RVE measurement should be in each case.

36 MATERIALS SCIENCE↗
DOE OSTI2014

2D stochastic-integral models for characterizing random grain noise in titanium alloys

We extend our previous work, in which we applied high-dimensional model representation (HDMR) and analysis of variance (ANOVA) concepts to the characterization of a metallic surface that has undergone a shot-peening treatment to reduce residual stresses, and has, therefore, become a random conductivity field. That example was treated as a onedimensional problem, because those were the only data available. In this study, we develop a more rigorous two-dimensional model for characterizing random, anisotropic grain noise in titanium alloys. Such a model is necessary if we are to accurately capture the 'clumping' of crystallites into long chains that appear during the processing of the metal into a finished product. The mathematical model starts with an application of the Karhunen-Loève (K-L) expansion for the random Euler angles, θ and φ, that characterize the orientation of each crystallite in the sample. The random orientation of each crystallite then defines the stochastic nature of the electrical conductivity tensor of the metal. We study two possible covariances, Gaussian and double-exponential, which are the kernel of the K-L integral equation, and find that the double-exponential appears to satisfy measurements more closely of the two. Results based on data from a Ti-7Al sample will be given, and further applications of HDMR and ANOVA will be discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Third Quantization and Emergence of the Quasiclassical Wave Function of the Universe

Quantized solutions of the Wheeler–DeWitt (WDW) equation describing a closed Friedmann–Robertson–Walker universe with a Λ term and a set of massless scalar fields are studied. It is shown that when Λ≪1 units and the standard in-vacuum state is considered, the wave function of the universe Ψ behaves as a random quasiclassical field at rather large a, namely, 1≪a≪e{sup (2/(3Λ))} [1].

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Bringing randomized algorithms to mainstream numerical linear algebra

Numerical linear algebra (NLA) underpins huge swaths of computational science and engineering. For scientists and engineers to make the most of the DOE’s computing resources, it is essential that they have access to high-performance implementations of algorithms with best-in-class scalability and reliability. Despite this, prevailing NLA libraries have little to no support for breakthrough algorithms from the field of randomized numerical linear algebra (RandNLA) that have been developed over the past twenty years. The goal of this LDRD was to break a log-jam that had prevented broad adoption of RandNLA. Our work had two thrusts. The first was to develop RandBLAS: a trustworthy and high-performance C++ library for randomized dimension reduction (an operation widely known as sketching). The second was the development of a novel randomized algorithm for computing a challenging type of matrix decomposition known as Householder QR with column pivoting (Householder QRCP). In this one-year late-start LDRD we successfully delivered RandBLAS 1.0 and new CPU and GPU codes for Householder QRCP. RandBLAS has extensive documentation at https://randblas.readthedocs.io/en/stable/. Papers on RandBLAS and and our high-performance QRCP codes are forthcoming.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Modeling the influence of preferential flow on the spatial variability and time-dependence of mineral weathering rates

Inferences of weathering rates from laboratory and field observations suggest significant scale and time-dependence. Preferential flow induced by heterogeneity (manifest as permeability variations or discrete fractures) has been suggested as one potential mechanism causing scale/time-dependence. In this paper, we present a quantitative evaluation of the influence of preferential flow on weathering rates using reactive transport modeling. Simulations were performed in discrete fracture networks (DFNs) and correlated random permeability fields (CRPFs), and compared to simulations in homogeneous permeability fields. The simulations reveal spatial variability in the weathering rate, multidimensional distribution of reactions zones, and the formation of rough weathering interfaces and corestones due to preferential flow. In the homogeneous fields and CRPFs, the domain-averaged weathering rate is initially constant as long as the weathering front is contained within the domain, reflecting equilibrium-controlled behavior. The behavior in the CRPFs was influenced by macrodispersion, with more spread-out weathering profiles, an earlier departure from the initial constant rate and longer persistence of weathering. DFN simulations exhibited a sustained time-dependence resulting from the formation of diffusion-controlled weathering fronts in matrix blocks, which is consistent with the shrinking core mechanism. A significant decrease in the domain-averaged weathering rate is evident despite high remaining mineral volume fractions, but the decline does not follow a math formula dependence, characteristic of diffusion, due to network scale effects and advection-controlled behavior near the inflow boundary. Finally, the DFN simulations also reveal relatively constant horizontally averaged weathering rates over a significant depth range, challenging the very notion of a weathering front.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Deconvolving the components of the sign problem

Auxiliary field quantum Monte Carlo simulations of interacting fermions require sampling over a Hubbard-Stratonovich field h introduced to decouple the interactions. The weight for a given configuration involves the products of the determinant of matrices $M_σ(h)$ where σ labels the species, and hence is typically not positive definite. Indeed, the average sign $\langle \mathscr {L} \rangle$ of the determinants goes to zero exponentially with increasing spatial size and decreasing temperature for most Hamiltonians of interest. This statement, however, does not explicitly separate two possible origins for the vanishing of $\langle \mathscr {L} \rangle$. Does $\langle \mathscr {L} \rangle$ → 0 because randomly chosen field configurations have det[M(h)] < 0, or does the sign problem arise because the specific subset of configurations chosen by the weighting function have a greater preponderance of negative values? In the latter case, the process of weighting the configurations with |det[M(h)]| might steer the simulation to a region of configuration space of h where positive and negative determinants are equally likely, even though randomly chosen h would preferentially have determinants with a single dominant sign. Here in this paper, we address the relative importance of these two mechanisms for the vanishing of $\langle \mathscr {L} \rangle$ in quantum simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2016

SOLAR CYCLE 25: ANOTHER MODERATE CYCLE?

Surface flux transport simulations for the descending phase of Cycle 24 using random sources (emerging bipolar magnetic regions) with empirically determined scatter of their properties provide a prediction of the axial dipole moment during the upcoming activity minimum together with a realistic uncertainty range. The expectation value for the dipole moment around 2020 (2.5 ± 1.1 G) is comparable to that observed at the end of Cycle 23 (about 2 G). The empirical correlation between the dipole moment during solar minimum and the strength of the subsequent cycle thus suggests that Cycle 25 will be of moderate amplitude, not much higher than that of the current cycle. However, the intrinsic uncertainty of such predictions resulting from the random scatter of the source properties is considerable and fundamentally limits the reliability with which such predictions can be made before activity minimum is reached.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

THE Ly{alpha} LINES OF H I AND He II: A DIFFERENTIAL HANLE EFFECT FOR EXPLORING THE MAGNETISM OF THE SOLAR TRANSITION REGION

The Ly{alpha} line of He II at 304 Angstrom-Sign is one of the spectral lines of choice for EUV channels of narrowband imagers on board space telescopes, which provide spectacular intensity images of the outer solar atmosphere. Since the magnetic field information is encoded in the polarization of the spectral line radiation, it is important to investigate whether the He II line radiation from the solar disk can be polarized, along with its magnetic sensitivity. Here we report some theoretical predictions concerning the linear polarization signals produced by scattering processes in this strong emission line of the solar transition region, taking into account radiative transfer and the Hanle effect caused by the presence of organized and random magnetic fields. We find that the fractional polarization amplitudes are significant ({approx}1%), even when considering the wavelength-integrated signals. Interestingly, the scattering polarization of the Ly{alpha} line of He II starts to be sensitive to the Hanle effect for magnetic strengths B {approx}> 100 G (i.e., for magnetic strengths of the order of and larger than the Hanle saturation field of the hydrogen Ly{alpha} line at 1216 Angstrom-Sign ). We therefore propose simultaneous observations of the scattering polarization in both Ly{alpha} lines to facilitate magnetic field measurements in the upper solar chromosphere. Even the development of a narrowband imaging polarimeter for the He II 304 Angstrom-Sign line alone would be already of great diagnostic value for probing the solar transition region.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Characterizing filamentary magnetic structures in counter-streaming plasmas by Fourier analysis of proton images

Proton imaging is a powerful tool for probing electromagnetic fields in a plasma, providing a path-integrated map of the field topology. However, in cases where the field structure is highly inhomogeneous, inferring spatial properties of the underlying field from proton images can be difficult. This problem is exemplified by recent experiments, which used proton imaging to probe the filamentary magnetic field structures produced by the Weibel instability in collisionless counterstreaming plasmas. In this paper, we perform analytical and numerical analyses of proton images of systems containing many magnetic filaments. We find that, in general, the features observed on proton images do not directly correspond to the spacing between magnetic filaments (the magnetic wavelength) as has previously been assumed and that they instead correspond to the filament size. Furthermore, we demonstrate this result by Fourier analysis of synthetic proton images for many randomized configurations of magnetic filaments. Our results help guide the interpretation of experimental proton images of filamentary magnetic structures in plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Disorder-induced local strain distribution in Y-substituted TmVO 4

We report an investigation of the effect of substitution of Y for Tm in Tm 1-x ⁢Y x VO 4 via low-temperature heat capacity measurements, with the yttrium content x varying from 0 to 0.997. Because the Tm ions support a local quadrupolar (nematic) moment, they act as reporters of the local strain state in the material, with the splitting of the ion's non-Kramers crystal field ground state proportional to the quadrature sum of the in-plane tetragonal symmetry-breaking transverse and longitudinal strains experienced by each ion individually. Analysis of the heat capacity, therefore, provides detailed insights into the distribution of local strains that arise as a consequence of the chemical substitution. These local strains suppress long-range quadrupole order for x > 0.22, and result in a broad Schottky-like feature for higher concentrations. Heat capacity data are compared to expectations for a distribution of uncorrelated (random) strains. For dilute Tm concentrations, the heat capacity cannot be accounted for by randomly distributed strains, demonstrating the presence of significant strain correlations between sites. For intermediate Tm concentrations, these correlations must still exist, but the data cannot be distinguished from that which would be obtained from a two-dimensional Gaussian distribution. The crossover between these limits is discussed in terms of the interplay of key lengthscales in the substituted material. Furthermore, the central result of this work, namely that local strains arising from chemical substitution are not uncorrelated, has implications for the range of validity of theoretical models based on random effective fields that are used to describe such chemically substituted materials, particularly when electronic nematic correlations are present.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation

The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of rogue wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A compressed sensing X-ray camera with a multilayer architecture

Recent advances in compressed sensing theory and algorithms offer new possibilities for high-speed X-ray camera design. In many CMOS cameras, each pixel has an independent on-board circuit that includes an amplifier, noise rejection, signal shaper, an analog-to-digital converter (ADC), and optional in-pixel storage. When X-ray images are sparse, i.e., when one of the following cases is true: (a.) The number of pixels with true X-ray hits is much smaller than the total number of pixels; (b.) The X-ray information is redundant; or (c.) Some prior knowledge about the X-ray images exists, sparse sampling may be allowed. In this work, we first illustrate the feasibility of random on-board pixel sampling (ROPS) using an existing set of X-ray images, followed by a discussion about signal to noise as a function of pixel size. Next, we describe a possible circuit architecture to achieve random pixel access and in-pixel storage. The combination of a multilayer architecture, sparse on-chip sampling, and computational image techniques, is expected to facilitate the development and applications of high-speed X-ray camera technology.

47 OTHER INSTRUMENTATION↗
DOE OSTI2013

SIMPLE ANALYTICAL FORMS OF THE PERPENDICULAR DIFFUSION COEFFICIENT FOR TWO-COMPONENT TURBULENCE. I. MAGNETOSTATIC TURBULENCE

We explore perpendicular diffusion based on the unified nonlinear transport theory. We derive simple analytical forms for the perpendicular mean free path and investigate the influence of different model spectra. We show that for cases where the field line random walk is normal diffusive, the perpendicular diffusion coefficient consists of only two transport regimes. Details of the spectral shape are less important, especially those of the inertial range. Only the macroscopic properties of the turbulence spectrum control the perpendicular diffusion coefficient. Simple formulae for the perpendicular diffusion coefficient are derived which can easily be implemented in solar modulation or shock acceleration codes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

97 MATHEMATICS AND COMPUTING↗