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DOE OSTI2020

Drag force to all orders in gradients

We study the energy loss of a heavy quark slowly moving through an evolving strongly coupled plasma. We use the linearized fluid/gravity correspondence to describe small perturbations of the medium flow with general spacetime dependence. This all order linearized hydrodynamics results in a drag force exerted on a heavy quark even when it is at rest with the fluid element. We show how the general contribution to the drag force can be derived order by order in the medium velocity gradients and provide explicit results valid up to the third order. We then obtain an approximate semi-analytic result for the drag force to all orders in the gradient expansion but linearized in the medium velocity. Thus, the effects of a class of hydrodynamic gradients on the drag force are re-summed, giving further insight into the dissipative properties of strongly coupled plasmas. The all order result allows us to study the drag force in the non-hydrodynamic regime of linear medium perturbations that vary rapidly in space and time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1988

A semianalytical technique for sensitivity analysis of unsteady aerodynamic computations

A semianalytical approach is developed for the sensitivity analysis of linear unsteady aerodynamic loads. The semianalytical approach is easier to implement than the analytical approach. It is also computationally less expensive than the finite difference approach when used with panel methods, which require a large number of panels. The semianalytical approach is applied to an isolated airfoil in a 2-D flow and rotating propfan blades in 3-D flow. Sensitivity coefficients with respect to non-shape-dependent variables are shown for some cases. It is expected that the semianalytical approach will be useful in aeroelastic design procedures particularly when mistuning is present, and that it is potentially useful for shape sensitivity analysis of linear unsteady aerodynamics.

Murthy, Durbha V.↗

DOE OSTI2018

Design of a One-Dimensional Sextupole Using Semi-Analytic Methods

Sextupole magnets provide position-dependent momentum kicks and are tuned to provide the correct kicks to parti- cles within a small acceptance region in phase space. Sextupoles are useful and even necessary in circular accelerators for chromaticity corrections. They are routinely used in most rings, i.e. CESR. Although sextupole magnets are necessary for particle energy corrections, they also have undesirable effects on dynamic aperture, especially because of their non- linear coupling term in the momentum kick. Studies of integrable systems suggest that there is an analytic way to create transport lattices with specific transfer matrices that limit the momentum kick to one dimension. A one-dimension sex- tupole is needed for chromaticity corrections: a horizontal sextupole for horizontal bending magnets. We know how to make a “composite” horizontal sextupole using regular 2D sextupoles and linear transfer matrices in an ideal thin-lens approximation. Thus, one could create an accelerator lattice using linear elements, in series with sextupole magnets to create a “1D sextupole”. This paper describes progress to- wards realizing a realistic focusing lattice resulting in a 1D sextupole.

43 PARTICLE ACCELERATORS↗

DOE OSTI2014

Linear Vlasov theory in the shearing sheet approximation with application to the magneto-rotational instability

We derive the conductivity tensor for axisymmetric perturbations of a hot, collisionless, and charge-neutral plasma in the shearing sheet approximation. Our results generalize the well-known linear Vlasov theory for uniform plasmas to differentially rotating plasmas and can be used for wide range of kinetic stability calculations. We apply these results to the linear theory of the magneto-rotational instability (MRI) in collisionless plasmas. We show analytically and numerically how the general kinetic theory results derived here reduce in appropriate limits to previous results in the literature, including the low-frequency guiding center (or 'kinetic MHD') approximation, Hall magnetohydrodynamics (MHD), and the gyro-viscous approximation. We revisit the cold plasma model of the MRI and show that, contrary to previous results, an initially unmagnetized collisionless plasma is linearly stable to axisymmetric perturbations in the cold plasma approximation. In addition to their application to astrophysical plasmas, our results provide a useful framework for assessing the linear stability of differentially rotating plasmas in laboratory experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Analytic marginalization of N(z) uncertainties in tomographic galaxy surveys

In this paper, we present a new method to marginalize over uncertainties in redshift distributions, N(z), within tomographic cosmological analyses applicable to current and upcoming photometric galaxy surveys. We allow for arbitrary deviations from the best-guess N(z) governed by a general covariance matrix describing the uncertainty in our knowledge of redshift distributions. In principle, this is marginalization over hundreds or thousands of new parameters describing potential deviations as a function of redshift and tomographic bin. However, by linearly expanding the theory predictions around a fiducial model, this marginalization can be performed analytically, resulting in a modified data covariance matrix that effectively downweights the modes of the data vector that are more sensitive to redshift distribution variations. We showcase this method by applying it to the galaxy clustering measurements from the Hyper Suprime-Cam first data release. We illustrate how to marginalize over sample variance of the calibration sample and a large general systematic uncertainty in photometric estimation methods, and explore the impact of priors imposing smoothness in the redshift distributions.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

TH-CD-207B-05: Measurement of CT Bow-Tie Profiles Using a Linear Array Detector

Purpose: To accurately measure CT bow-tie profiles from various manufacturers and to provide non-proprietary information for CT system modeling. Methods: A GOS-based linear detector (0.8 mm per pixel and 51.2 cm in length) with a fast data sampling speed (0.24 ms/sample) was used to measure the relative profiles of bow-tie filters from a collection of eight CT scanners by three different vendors, GE (LS Xtra, LS VCT, Discovery HD750), Siemens (Sensation 64, Edge, Flash, Force), and Philips (iBrilliance 256). The linear detector was first calibrated for its energy response within typical CT beam quality ranges and compared with an ion chamber and analytical modeling (SPECTRA and TASMIP). A geometrical calibration process was developed to determine key parameters including the distance from the focal spot to the linear detector, the angular increment of the gantry at each data sampling, the location of the central x-ray on the linear detector, and the angular response of the detector pixel. Measurements were performed under axial-scan modes for most representative bow-tie filters and kV selections from each scanner. Bow-tie profiles were determined by re-binning the measured rotational data with an angular accuracy of 0.1 degree using the calibrated geometrical parameters. Results: The linear detector demonstrated an energy response as a solid state detector, which is close to the CT imaging detector. The geometrical calibration was proven to be sufficiently accurate (< 1mm in error for distances >550 mm) and the bow-tie profiles measured from rotational mode matched closely to those from the gantry-stationary mode. Accurate profiles were determined for a total of 21 bow-tie filters and 83 filter/kV combinations from the abovementioned scanner models. Conclusion: A new improved approach of CT bow-tie measurement was proposed and accurate bow-tie profiles were provided for a broad list of CT scanner models.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2014

Comparison of two-fluid and gyrokinetic models for kinetic Alfvén waves in solar and space plasmas

An analytical comparative study of a two-fluid and a gyrokinetic model of kinetic Alfvén waves (KAWs) is presented for various solar and space plasma environments. Based on the linear KAW dispersion relation for gyrokinetics (Howes et al. 2006), the wave group velocity and electromagnetic polarizations are obtained analytically. Then the gyrokinetic wave properties are compared with those of the two-fluid model. The results show that both models agree well with each other not only in the long wavelength regime (>> the ion gyroradius ρ {sub i}) for all cases considered, but also in wavelengths ∼ρ {sub i} and <<ρ {sub i} (still much larger than the electron gyroscale) for a moderate or low (≲ 1) and a high (>>1) ion/electron temperature ratio T {sub 0i}/T {sub 0e}, respectively. However, the fluid model calculations deviate strongly from the gyrokinetic model at scales <ρ {sub i} for a relatively low T {sub 0i}/T {sub 0e} due to the electron gyroradius effect. Meanwhile, the plasma β {sub i} can make the gyrokinetic dispersion relation of KAWs become complex and sometimes have an oscillation-like structure. With the inherent simplicity of the fluid theory, these results may improve our understanding of the applicability of the two-fluid model, and may have important implications for computer simulation studies of KAWs in the solar and space plasma surroundings.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Self-assembly and glass-formation in a lattice model of telechelic polymer melts: Influence of stiffness of the sticky bonds

Telechelic polymers are chain macromolecules that may self-assemble through the association of their two mono-functional end groups (called “stickers”). A deep understanding of the relation between microscopic molecular details and the macroscopic physical properties of telechelic polymers is important in guiding the rational design of telechelic polymer materials with desired properties. The lattice cluster theory (LCT) for strongly interacting, self-assembling telechelic polymers provides a theoretical tool that enables establishing the connections between important microscopic molecular details of self-assembling polymers and their bulk thermodynamics. The original LCT for self-assembly of telechelic polymers considers a model of fully flexible linear chains [J. Dudowicz and K. F. Freed, J. Chem. Phys. 136, 064902 (2012)], while our recent work introduces a significant improvement to the LCT by including a description of chain semiflexibility for the bonds within each individual telechelic chain [W.-S. Xu and K. F. Freed, J. Chem. Phys. 143, 024901 (2015)], but the physically associative (or called “sticky”) bonds between the ends of the telechelics are left as fully flexible. Motivated by the ubiquitous presence of steric constraints on the association of real telechelic polymers that impart an additional degree of bond stiffness (or rigidity), the present paper further extends the LCT to permit the sticky bonds to be semiflexible but to have a stiffness differing from that within each telechelic chain. An analytical expression for the Helmholtz free energy is provided for this model of linear telechelic polymer melts, and illustrative calculations demonstrate the significant influence of the stiffness of the sticky bonds on the self-assembly and thermodynamics of telechelic polymers. A brief discussion is also provided for the impact of self-assembly on glass-formation by combining the LCT description for this extended model of telechelic polymers with the Adam-Gibbs relation between the structural relaxation time and the configurational entropy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1987

Static and dynamic characteristics of parallel-grooved seals

Presented is an analytical method to determine static and dynamic characteristics of annular parallel-grooved seals. The governing equations were derived by using the turbulent lubrication theory based on the law of fluid friction. Linear zero- and first-order perturbation equations of the governing equations were developed, and these equations were analytically investigated to obtain the reaction force of the seals. An analysis is presented that calculates the leakage flow rate, the torque loss, and the rotordynamic coefficients for parallel-grooved seals. To demonstrate this analysis, we show the effect of changing number of stages, land and groove width, and inlet swirl on stability of the boiler feed water pump seals. Generally, as the number of stages increased or the grooves became wider, the leakage flow rate and rotor-dynamic coefficients decreased and the torque loss increased.

Iwatsubo, Takuzo↗

NASA NTRS1993

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.

Buchert, T.↗

DOE OSTI2024

Deep eutectic solvents as green and sustainable diluents in headspace gas chromatography for the determination of trace level genotoxic impurities in pharmaceuticals

Genotoxic impurities (GTIs) are potential carcinogens that need to be controlled down to ppm or lower concentration levels in pharmaceuticals under strict regulations. The static headspace gas chromatography (HS-GC) coupled with electron capture detection (ECD) is an effective approach to monitor halogenated and nitroaromatic genotoxins. Deep eutectic solvents (DESs) possess tunable physico-chemical properties and low vapor pressure for HS-GC methods. In this study, zwitterionic and non-ionic DESs have been used for the first time to develop and validate a sensitive analytical method for the analysis of 24 genotoxins at sub-ppm concentrations. Compared to non-ionic diluents, zwitterionic DESs produced exceptional analytical performance and the betaine: 7 (1,4- butane diol) DES outperformed the betaine: 5 (1,4-butane diol) DES. Limits of detection (LOD) down to the 5-ppb concentration level were achieved in DESs. Wide linear ranges spanning over 5 orders of magnitude (0.005–100 µg g –1 ) were obtained for most analytes with exceptional sensitivities and high precision. The method accuracy and precision were validated using 3 commercially available drug substances and excellent recoveries were obtained. Finally, this study broadens the applicability of HS-GC in the determination of less volatile GTIs by establishing DESs as viable diluent substitutes for organic solvents in routine pharmaceutical analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2006

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Gnoffo, Peter A.↗

DOE OSTI2026

Analytic model for neutral penetration and plasma fueling

Neutral atoms recycled from wall interaction interact with confined plasma, thereby refuelling it, most strongly in the region closest to the wall. This occurs near the X-point in diverted configurations, or else near the wall itself in limited configurations. A progression of analytic models is developed for neutral density in the vicinity of a planar or linear source in an ionising domain. First-principles neutral transport simulations with DEGAS2 are used throughout to test the validity and limits of the model when using equivalent sources. The model is further generalised for strong plasma gradients or the inclusion of charge exchange. An important part of the problem of neutral fuelling from recycling is thereby isolated and solved with a closed-form analytic model. A key finding is that charge exchange with the confined plasma can be significantly simplified with a reasonable sacrifice of accuracy by treating it as a loss. The several assumptions inherent to the model (and the simulations with which it is compared) can be adapted according to the particular behaviour of neutrals in the divertor and the manner in which they cross the separatrix.

fusion plasma↗

NASA NTRS2010

Verifiable Adaptive Control with Analytical Stability Margins by Optimal Control Modification

This paper presents a verifiable model-reference adaptive control method based on an optimal control formulation for linear uncertain systems. A predictor model is formulated to enable a parameter estimation of the system parametric uncertainty. The adaptation is based on both the tracking error and predictor error. Using a singular perturbation argument, it can be shown that the closed-loop system tends to a linear time invariant model asymptotically under an assumption of fast adaptation. A stability margin analysis is given to estimate a lower bound of the time delay margin using a matrix measure method. Using this analytical method, the free design parameter n of the optimal control modification adaptive law can be determined to meet a specification of stability margin for verification purposes.

Nguyen, Nhan T.↗

NASA NTRS1985

An experimental and analytical investigation of isolated rotor flap-lag stability in forward flight

For flap-lag stability of isolated rotors, experimental and analytical investigations are conducted in hover and forward flight on the adequacy of a linear quasi-steady aerodynamics theory with dynamic inflow. Forward flight effects on lag regressing mode are emphasized. Accordingly, a soft inplane hingeless rotor with three blades is tested at advance ratios as high as 0.55 and at shaft angles as high as 20 deg. The 1.62-m model rotor is untrimmed with an essentially unrestricted tilt of the tip path plane. By computerized symbolic manipulation, an analytical model is developed in substall to predict stability margins with mode indentification. It also predicts substall and stall regions to help explain the correlation between theory and data. The correlation shows both the strengths and weaknesses of the data and theory, and promotes further insights into areas in which further study is needed in substall and stall.

Gaonkar, Gopal H.↗

NASA NTRS1983

Calculation of unsteady small disturbance transonic flow at arbitrary reduced frequency using an extended integral equation method.

A novel analytical-numerical method for calculating unsteady small disturbance transonic flow over airfoils has been developed. The method uses an extended integral equation technique, based on both the velocity potential and the acceleration potential, to predict unsteady aerodynamic loading on airfoils oscillating in subcritical transonic free stream conditions. The formulation is an extension of the work of Sivaneri and Harris (1980) for steady, non-lifting flows and utilizes the linear theory of Landahl (1961) for decoupling of steady and unsteady components. The analytical-numerical procedure involves several intnegrating schemes and applies to general frequencies of oscillations. The technique is illustrated by computing the transonic flow about parabolic arc airfoils. Specific unsteady results for reduced frequencies based on semi-chord of 0.01, 0.1, 0.3, 0.4 and 0.6 are given. Comparison of results with those obtained by an ADI finite difference scheme is made.

Lamah, C. A.↗

NASA NTRS1993

Results from the Middeck 0-gravity Dynamics Experiment

The experimental results of the Middick Zero-gravity Dynamics Experiment (MODE) are presented. MODE investigated the dynamics of two key spacecraft components; contained fluids and jointed truss structures. The change in the lateral slosh behavior of contained fluids and the changes in the modal parameters of space structural test articles from one- to zero-gravity were studied. The experimental apparatus used to determine the dynamic characteristics is described. For the MODE fluid experiments, the forced response characteristics of silicone oil and distilled water in cylinder tanks with either a flat or spherical bottom are reported and discussed. A comparison of the measured earth and space results identifies and highlights the effects of gravity on the linear and nonlinear slosh behavior of these fluids. For the MODE structural experiments, an analytic and experimental study is presented. Deployable, erectable, and rotary modules were assembled to form three one- and two-dimensional structures in which variations in bracing wire and rotary joint preload could be introduced. Analysis is compared with ground experimental measurements made on a spring/wire suspension system with a nominal plunge frequency of one Hertz, and with measurements made on the Shuttle middeck. The degree of change in linear modal parameters as well as the change in nonlinear nature of the response is examined. Trends in modal parameters are presented as a function of force amplitude, joint preload, and ambient gravity level.

Van Schoor, M. C.↗

DOE OSTI2015

Scalar-fluid theories: cosmological perturbations and large-scale structure

Recently a new Lagrangian framework was introduced to describe interactions between scalar fields and relativistic perfect fluids. This allows two consistent generalizations of coupled quintessence models: non-vanishing pressures and a new type of derivative interaction. The implications of these to the formation of cosmological large-scale structure are uncovered here at the linear order. The full perturbation equations in the two cases are derived in a unified formalism and their Newtonian, quasi-static limit is studied analytically. Requiring the absence of an effective sound speed term in the coupled dark matter fluid restricts the Lagrangian to be a linear function of the matter number density. This leaves new potentially viable classes of both algebraically and derivatively interacting models wherein the coupling may impact the background expansion dynamics and imprint new signatures into the large-scale structure.

79 ASTRONOMY AND ASTROPHYSICS↗