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DOE OSTI2015

Future of the Beam Energy Scan program at RHIC

The first exploratory phase of a very successful Beam Energy Scan Program at RHIC was completed in 2014 with Au+Au collisions at energies ranging from 7 to 39 GeV. Data sets taken earlier extended the upper limit of energy range to the √sNN of 200 GeV. This provided an initial look into the uncharted territory of the QCD phase diagram, which is considered to be the single most important graph of our field. The main results from BES phase I, although effected by large statistical errors (steeply increasing with decreasing energy), suggest that the highest potential for discovery of the QCD Critical Point lies bellow √sNN 20 GeV. Here, we discuss the plans and the preparation for phase II of the BES program, with an order of magnitude larger statistics, which is planned for 2018-2019. The BES II will focus on Au+Au collisions at √sNN from 20 to 7 GeV in collider mode, and from √sNN 7 to 3.5 GeV in the fixed target mode, which will be run concurrently with the collider mode operation.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Monotonic multi-state quantum f -divergences

We use the Tomita–Takesaki modular theory and the Kubo–Ando operator mean to write down a large class of multi-state quantum f-divergences and prove that they satisfy the data processing inequality. For two states, this class includes the (α, z)-Rényi divergences, the f-divergences of Petz, and the Rényi Belavkin-Staszewski relative entropy as special cases. The method used is the interpolation theory of non-commutative Lωp spaces, and the result applies to general von Neumann algebras, including the local algebra of quantum field theory. We conjecture that these multi-state Rényi divergences have operational interpretations in terms of the optimal error probabilities in asymmetric multi-state quantum state discrimination.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2011

Studies of the Effects of Optical System Errors on the HCIT Contrast Performance

The High Contrast Imaging Testbed (HCIT) at the Jet Propulsion Laboratory employs a broadband wavefront correction algorithm called Electric Field Conjugation (EFC) to obtain the required 10-10 contrast. This algorithm works with one deformable mirror (DM) to estimate the electric-field to be controlled, and with one or multiple DM's to create a "dark-hole" in a predefined region of the image plane where terrestrial planets would be found. We have investigated the effects of DM actuator errors and the optic position errors on the efficiency of the EFC algorithm in a Lyot coronagraph configuration. The structural design of the optical system as well as the parameters of various optical elements used in the analysis are drawn from those of the HCIT system that have been implemented with one DM. The simulation takes into account the surface errors of various optical elements. Results of some of these studies have been verified by actual measurements.

exoplanetsscopes↗

DOE OSTI2013

SIMULATED FARADAY ROTATION MEASURES TOWARD HIGH GALACTIC LATITUDES

We study the Faraday rotation measure (RM) due to the Galactic magnetic field (GMF) toward high Galactic latitudes. The RM arises from the global, regular component as well as from the turbulent, random component of the GMF. We model the former based on observations and the latter using the data of magnetohydrodynamic turbulence simulations. For a large number of different GMF models, we produce mock RM maps around the Galactic poles and calculate various statistical quantities with the RM maps. We find that the observed medians of RMs toward the north and south Galactic poles, {approx}0.0 {+-} 0.5 rad m{sup -2} and {approx} + 6.3 {+-} 0.5 rad m{sup -2}, are difficult to explain with any of our many alternate GMF models. The standard deviation of observed RMs, {approx}9 rad m{sup -2}, is clearly larger than that of simulated RMs. The second-order structure function of observed RMs is substantially larger than that of simulated RMs, especially at small angular scales. We discuss other possible contributions to RM toward high Galactic latitudes. Besides observational errors and the intrinsic RM of background radio sources against which RM is observed, we suggest that the RM due to the intergalactic magnetic field may account for a substantial fraction of the observed RM. Finally, we note that reproducing the observed medians may require additional components or/and structures of the GMF that are not present in our models.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Particle-image Velocimetry Sensitivity through Automatic Differentiation

A commonly encountered difficulty in modern experimental fluid dynamics experiments is the need for full-flow visualization and measurement; traditional techniques such as hot-wire probes and laser Doppler velocimetry cannot provide such information without difficult scanning procedures. Particle-image velocimetry (PIV) is a measurement technique which can overcome this spatial limitation to provide real-time three-dimensional fluid velocity vectors for an entire plane within the flow, as opposed to a single point that is provided by other measurement techniques. To accomplish this, a PIV system seeds the fluid flow with tracer particles; these must have nearly the same density as that of the fluid and a high drag coefficient to ensure that they follow the fluid flow without deviation. A laser is sent through optics to expand its beam into a sheet which illuminates the plane of interest in the fluid. The particles reflect more light than the fluid, and their image is recorded using a high speed camera. Due to limitations in bandwidth, video cannot be taken fast enough to be useful, and instead pairs of images are captured with a known separation in time. The illuminated particles will move between the two images taken by the camera, and their relative motion can be used to compute the fluid velocity at that point. When a single camera is used, only two-dimensional velocity vectors can be computed, but with the addition of another camera this can be improved to full three-dimensional vectors. The flow's time evolution can be measured by taking series of image pairs and processing each pair to get the velocity field at the time between each image pair. Only the two-dimensional version will be considered in this work. To compute the velocity vectors of the flow, the images are broken up into interrogation regions, usually in a uniform grid. In the most basic PIV algorithm, corresponding regions in the image pairs are cross-correlated to compute the most likely displacement from one image to the next. This is used since the cross correlation will achieve a maximum value when the two interrogation regions line up the best. The location of the peak in the correlation map and scaling information for the optical setup is used to compute the particle displacement from one image to the next. This process is similar to holding two semi-transparent images and moving one until they match as well as possible. Sub-pixel displacements between images can be obtained by fitting a Gaussian function to the correlation peak. Knowing the displacement vector for each set of interrogation regions in the image pair, it is a simple matter to divide by the time gap between the two images to compute the fluid velocity at the point in time and space. Since there are many interrogation regions in each image pair, the velocity field for a sheet is sampled according to the arrangement of the interrogation regions. The sensitivity of the final computed vector to the input images is difficult to compute, and has led most considerations of uncertainty in the PIV field to apply Monte Carlo methods and correlations to quantify the systematic and random errors which result from application of various PIV algorithms. In this work, automatic differentiation (AD) has been used to trace the dependence of velocity vectors computed using the correlation-peak PIV algorithm back to the input values given to an artificial image generator. These initial results form the foundation for continued work in the application of AD to algorithms in PIV. They demonstrate that AD methods can be successfully applied to PIV algorithms without undue complexity. The derivatives of each individual vector with regard to the coefficients of the velocity field used to create the artificial images can be computed and the statistics of them considered collectively, or correlated between each other to quantify the effectiveness of a PIV algorithm. With the initial implementation complete, adding extra algorithms is relatively simple and considerable data can be generated for analysis. It is hoped that application of these methods can lead to improved PIV algorithms which demonstrate better sensitivity to small variations in particle displacement. While these methods can be used as an analysis tool for refinement of new algorithms, computation of actual resultant vector sensitivities to input images' individual pixels is the next logical step of this work. Such information will be analyzed with experimental data to produce a better understanding of how output vectors' uncertainty relates to the actual image pairs, and lead to automatic bad vector removal. (authors)

42 ENGINEERING↗

DOE OSTI2016

SU-G-BRC-17: Using Generalized Mean for Equivalent Square Estimation

Purpose: Equivalent Square (ES) is a widely used concept in radiotherapy. It enables us to determine many important quantities for a rectangular treatment field, without measurement, based on the corresponding values from its ES field. In this study, we propose a Generalized Mean (GM) type ES formula and compare it with other established formulae using benchmark datasets. Methods: Our GM approach is expressed as ES=(w•fx^α+(1-w)•fy^α)^(1/α), where fx, fy, α, and w represent field sizes, power index, and a weighting factor, respectively. When α=−1 it reduces to well-known Sterling type ES formulae. In our study, α and w are determined through least-square-fitting. Akaike Information Criterion (AIC) was used to benchmark the performance of each formula. BJR (Supplement 17) ES field table for X-ray PDDs and open field output factor tables in Varian TrueBeam representative dataset were used for validation. Results: Switching from α=−1 to α=−1.25, a 20% reduction in standard deviation of residual error in ES estimation was achieved for the BJR dataset. The maximum relative residual error was reduced from ∼3% (in Sterling formula) or ∼2% (in Vadash/Bjarngard formula) down to ∼1% in GM formula for open fields of all energies and at rectangular field sizes from 3cm to 40cm in the Varian dataset. The improvement of the GM over the Sterling type ES formulae is particularly noticeable for very elongated rectangular fields with short width. AIC analysis confirmed the superior performance of the GM formula after taking into account the expanded parameter space. Conclusion: The GM significantly outperforms Sterling type formulae at slightly increased computational cost. The GM calculation may nullify the requirement of data measurement for many rectangular fields and hence shorten the Linac commissioning process. Improved dose calculation accuracy is also expected by adopting the GM formula into treatment planning and secondary MU check systems.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2014

Finite-difference schemes for anisotropic diffusion

In fusion plasmas diffusion tensors are extremely anisotropic due to the high temperature and large magnetic field strength. This causes diffusion, heat conduction, and viscous momentum loss, to effectively be aligned with the magnetic field lines. This alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to 10{sup 12} times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. Currently the common approach is to apply magnetic field-aligned coordinates, an approach that automatically takes care of the directionality of the diffusive coefficients. This approach runs into problems at x-points and at points where there is magnetic re-connection, since this causes local non-alignment. It is therefore useful to consider numerical schemes that are tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this, in this paper several discretization schemes are developed and applied to the anisotropic heat diffusion equation on a non-aligned grid.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1982

A technique for measuring magnetic fields on solar-type stars

A method is developed and tested by which magnetic-field strengths and area filling-factors of magnetic regions on late-type stars may be inferred from high-resolution, absorption-line profiles that have been broadened by the Zeeman effect. The technique involves fitting such profiles with a triplet of components, the shape of which is derived from profiles of lines of low Zeeman sensitivity. Tests of the systematic and random errors indicate that such magnetic flux measurements have an uncertainty of 20% for stars with field strengths of 2000 gauss if at least 10% of the stellar surface contains magnetic regions.

Marcy, G. W.↗

NASA NTRS1990

Model-based estimation of wind fields over the ocean from wind scatterometer measurements. I - Development of the wind field model. II - Model parameter estimation

Techniques for the determination of near-surface mesoscale ocean wind fields on the basis of satellite scatterometer data are developed and demonstrated. The derivation of normal-boundary and parameterized-boundary-condition (PBC) wind-field models is outlined, and results from a simulation performed to estimate the model errors are presented in tables. It is shown that the PBC model provides accurate results while minimizing the number of unknowns. After a review of the principles of scatterometry and an analysis of scatterometer measurement noise, an objective function for the measurement parameters is developed and optimized on the basis of gradient search with initial values computed from pointwise wind estimates. The model is then applied to data from a simulation of the NASA Scatterometer (Li et al., 1984), and the results are presented in extensive graphs. The feasibility of model-based wind-field estimation and the appropriateness of the PBC model are demonstrated.

Long, David G.↗

NASA NTRS2014

CM5, a Pre-Swarm Comprehensive Geomagnetic Field Model Derived from Over 12 Yr of CHAMP, Orsted, SAC-C and Observatory Data

A comprehensive magnetic field model named CM5 has been derived from CHAMP, Ørsted and SAC-C satellite and observatory hourly-means data from 2000 August to 2013 January using the Swarm Level-2 Comprehensive Inversion (CI) algorithm. Swarm is a recently launched constellation of three satellites to map the Earth's magnetic field. The CI technique includes several interesting features such as the bias mitigation scheme known as Selective Infinite Variance Weighting (SIVW), a new treatment for attitude error in satellite vector measurements, and the inclusion of 3-D conductivity for ionospheric induction. SIVW has allowed for a much improved lithospheric field recovery over CM4 by exploiting CHAMP along-track difference data yielding resolution levels up to spherical harmonic degree 107, and has allowed for the successful extraction of the oceanic M2 tidal magnetic field from quiet, nightside data. The 3-D induction now captures anomalous Solar-quiet features in coastal observatory daily records. CM5 provides a satisfactory, continuous description of the major magnetic fields in the near-Earth region over this time span, and its lithospheric, ionospheric and oceanic M2 tidal constituents may be used as validation tools for future Swarm Level-2 products coming from the CI algorithm and other dedicated product algorithms.

modelling and interpretation↗

NASA NTRS1978

A decoding procedure for the Reed-Solomon codes

A decoding procedure is described for the (n,k) t-error-correcting Reed-Solomon (RS) code, and an implementation of the (31,15) RS code for the I4-TENEX central system. This code can be used for error correction in large archival memory systems. The principal features of the decoder are a Galois field arithmetic unit implemented by microprogramming a microprocessor, and syndrome calculation by using the g(x) encoding shift register. Complete decoding of the (31,15) code is expected to take less than 500 microsecs. The syndrome calculation is performed by hardware using the encoding shift register and a modified Chien search. The error location polynomial is computed by using Lin's table, which is an interpretation of Berlekamp's iterative algorithm. The error location numbers are calculated by using the Chien search. Finally, the error values are computed by using Forney's method.

Lim, R. S.↗

DOE OSTI2017

Numerical Uncertainties vs. Model Uncertainties in Two-phase Flow Simulations

In recent years, verification, validation and uncertainty quantification (VVUQ) have become a common practice in thermal-hydraulics analysis. In general, these activities deal with propagations of uncertainties in computer code simulations, e.g., through system analysis codes. However, most existing such activities in thermal-hydraulics analysis have been primarily focused on model uncertainties, while numerical uncertainties were largely overlooked. Numerical uncertainties (or numerical errors) can appear in many different forms, e.g., round-off error, statistical sampling error, and discretization error. As pointed out by Oberkampf and Roy, discretization error is usually the largest however the most difficult type of error to estimate reliably. In thermal-hydraulics analysis, especially two-phase flow simulations commonly encountered in reactor safety analysis, the lack of consideration on discretization error is mainly due to the difficulty in estimating them. Accurate estimations on discretization error require continuous mesh refinement and/or implementation of high-order numerical schemes in system analysis code, both of which are unfortunately difficult to achieve for existing codes. At first, it should be emphasized that mesh refinement (or mesh sensitivity study) is a well-understood concept in the thermal-hydraulics field. However, it is not commonly practiced for many reasons, e.g., lack of understanding on numerical errors by code users, consideration on computational cost, deteriorated numerical stability performance with refined meshes, and etc. Secondly, high-order (e.g., second-order) numerical schemes are simply unavailable in almost any existing system analysis code. Implementation of high-order numerical schemes in these codes is difficult, if not impossible, given the complexity of these codes. On the other hand, people tend to argue that numerical uncertainties (or discretization error as we have emphasized) are not as important as the commonly large uncertainties in two-phase flow models, e.g., closure correlations. As a result, nodalization is sometimes played unintentionally, or maybe intentionally, to match experimental data, which is referred as 'user effects' or 'compensating errors' in thermal-hydraulics community. Such a practice is highly criticized by Levy. In this work, we will at first build a computer code that incorporates both first-order and second-order numerical methods to solve the two-phase flow problems. The first-order method resembles the one used in many existing system analysis codes; and the second-order method works as the reference to estimate numerical errors. Numerical verifications on spatial discretization schemes will be presented in the form of mesh convergence study. It will also be demonstrated that, in practical scenarios, discretization errors can be as large as, or even larger than, model uncertainties via case studies.

42 ENGINEERING↗

DOE OSTI2023

Size-dependent errors in real-time electron density propagation

Real-time (RT) electron density propagation with time-dependent density functional theory (TDDFT) or Hartree–Fock (TDHF) is one of the most popular methods to model the charge transfer in molecules and materials. However, both RT-TDHF and RT-TDDFT within the adiabatic approximation are known to produce inaccurate evolution of the electron density away from the ground state in model systems, leading to large errors in charge transfer and erroneous shifting of peaks in absorption spectra. Given the poor performance of these methods with small model systems and the widespread use of the methods with larger molecular and material systems, here we bridge the gap in our understanding of these methods and examine the size-dependence of errors in RT density propagation. We analyze the performance of RT density propagation for systems of increasing size during the application of a continuous resonant field to induce Rabi-like oscillations, during charge-transfer dynamics, and for peak shifting in simulated absorption spectra. We find that the errors in the electron dynamics are indeed size dependent for these phenomena, with the largest system producing the results most aligned with those expected from linear response theory. The results suggest that although the RT-TDHF and RT-TDDFT methods may produce severe errors for model systems, the errors in charge transfer and resonantly driven electron dynamics may be much less significant for more realistic, large-scale molecules and materials.

Chemistry↗

DOE OSTI2024

Iterative Stress Reconstruction Algorithm to Estimate Three-Dimensional Residual Stress Fields in Manufactured Components

Residual stress (RS) significantly impacts the mechanical performance of components. Measurement of RS often provides incomplete data in terms of components of stress and spatial density. Employing such fields in finite element simulations results in significant modification of the field to achieve equilibrium and compatibility among strains. To overcome this, an iterative stress reconstruction algorithm (ISRA) is developed to estimate 3D RS fields that satisfy equilibrium, are stress component-wise complete, and represent the characterized data sampled. An Al 7075-T651 plate and an additively manufactured (AM) A36 steel wall are considered for RS reconstruction using measurement data from the literature. A maximum variation of ~2.5 MPa in the Al plate, and ~10 MPa in the steel wall are observed between the reconstructed and measured stresses. Furthermore, unknown stress components emerge and reach significant magnitudes (upto ~2.3 MPa in the Al plate and ~45 MPa in the AM wall) during ISRA. Indeed, it is found that minor errors in measurement or data processing are eliminated through the physical requirements during ISRA. Employing a reconstructed RS field is hence not just more accurate given its compatibility, but it additionally corrects for minor errors in measurement. Furthermore, it is found that spatially dense measurement data result in convergence with fewer iterations. Finally, although ISRA yields a nonunique solution dependent on boundary conditions, measurement errors, fitting errors, and mesh density, it accommodates for uncertainties and inaccuracies in measurement, as opposed to failing to reach a physically realistic converged solution.

42 ENGINEERING↗

NASA NTRS1971

A Quantitative Evaluation of Dissolved Oxygen Instrumentation

The implications of the presence of dissolved oxygen in water are discussed in terms of its deleterious or beneficial effects, depending on the functional consequences to those affected, e.g., the industrialist, the oceanographer, and the ecologist. The paper is devoted primarily to an examination of the performance of five commercially available dissolved oxygen meters. The design of each is briefly reviewed and ease or difficulty of use in the field described. Specifically, the evaluation program treated a number of parameters and user considerations including an initial check and trial calibration for each instrument and a discussion of the measurement methodology employed. Detailed test results are given relating to the effects of primary power variation, water-flow sensitivity, response time, relative accuracy of dissolved-oxygen readout, temperature accuracy (for those instruments which included this feature), error and repeatability, stability, pressure and other environmental effects, and test results obtained in the field. Overall instrument performance is summarized comparatively by chart.

Pijanowski, Barbara S.↗

DOE OSTI2016

New constraints on modelling the random magnetic field of the MW

We extend the description of the isotropic and anisotropic random component of the small-scale magnetic field within the existing magnetic field model of the Milky Way from Jansson and Farrar, by including random realizations of the small-scale component. Using a magnetic-field power spectrum with Gaussian random fields, the NE2001 model for the thermal electrons and the Galactic cosmic-ray electron distribution from the current GALPROP model we derive full-sky maps for the total and polarized synchrotron intensity as well as the Faraday rotation-measure distribution. While previous work assumed that small-scale fluctuations average out along the line-of-sight or which only computed ensemble averages of random fields, we show that these fluctuations need to be carefully taken into account. Comparing with observational data we obtain not only good agreement with 408 MHz total and WMAP7 22 GHz polarized intensity emission maps, but also an improved agreement with Galactic foreground rotation-measure maps and power spectra, whose amplitude and shape strongly depend on the parameters of the random field. We demonstrate that a correlation length of 0≈22 pc (05 pc being a 5σ lower limit) is needed to match the slope of the observed power spectrum of Galactic foreground rotation-measure maps. Using multiple realizations allows us also to infer errors on individual observables. We find that previously-used amplitudes for random and anisotropic random magnetic field components need to be rescaled by factors of ≈0.3 and 0.6 to account for the new small-scale contributions. Our model predicts a rotation measure of −2.8±7.1 rad/m{sup 2} and 04.4±11. rad/m{sup 2} for the north and south Galactic poles respectively, in good agreement with observations. Applying our model to deflections of ultra-high-energy cosmic rays we infer a mean deflection of ≈3.5±1.1 degree for 60 EeV protons arriving from CenA.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Efficient field-theoretic simulation of polymer solutions

We present several developments that facilitate the efficient field-theoretic simulation of polymers by complex Langevin sampling. A regularization scheme using finite Gaussian excluded volume interactions is used to derive a polymer solution model that appears free of ultraviolet divergences and hence is well-suited for lattice-discretized field theoretic simulation. We show that such models can exhibit ultraviolet sensitivity, a numerical pathology that dramatically increases sampling error in the continuum lattice limit, and further show that this pathology can be eliminated by appropriate model reformulation by variable transformation. We present an exponential time differencing algorithm for integrating complex Langevin equations for field theoretic simulation, and show that the algorithm exhibits excellent accuracy and stability properties for our regularized polymer model. These developments collectively enable substantially more efficient field-theoretic simulation of polymers, and illustrate the importance of simultaneously addressing analytical and numerical pathologies when implementing such computations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1994

Field verification of the wind tunnel coefficients

Accurate information about wind action on antennas is required for reliable prediction of antenna pointing errors in windy weather and for the design of an antenna controller with wind disturbance rejection properties. The wind tunnel data obtained 3 years ago using a scaled antenna model serves as an antenna industry standard, frequently used for the first purpose. The accuracy of the wind tunnel data has often been challenged, since they have not yet been tested in a field environment (full-aized antenna, real wind, actual terrain, etc.). The purpose of this investigation was to obtain selected field measurements and compare them with the available wind tunnel data. For this purpose, wind steady-state torques of the DSS-13 antenna were measured, and dimensionless wind torque coefficients were obtained for a variety of yaw and elevation angles. The results showed that the differences between the wind tunnel torque coefficients and the field torque coefficients were less than 10 percent of their values. The wind-gusting action on the antenna was characterized by the power spectra of the antenna encoder and the antenna torques. The spectra showed that wind gusting primarily affects the antenna principal modes.

Gawronski, W. K.↗