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DOE OSTI2016

THE PARKER INSTABILITY IN DISK GALAXIES

We examine the evolution of the Parker instability in galactic disks using 3D numerical simulations. We consider a local Cartesian box section of a galactic disk, where gas, magnetic fields, and cosmic rays are all initially in a magnetohydrostatic equilibrium. This is done for different choices of initial cosmic-ray density and magnetic field. The growth rates and characteristic scales obtained from the models, as well as their dependences on the density of cosmic rays and magnetic fields, are in broad agreement with previous (linearized, ideal) analytical work. However, this nonideal instability develops a multimodal 3D structure, which cannot be quantitatively predicted from the earlier linearized studies. This 3D signature of the instability will be of importance in interpreting observations. As a preliminary step toward such interpretations, we calculate synthetic polarized intensity and Faraday rotation measure (RM) maps, and the associated structure functions of the latter, from our simulations; these suggest that the correlation scales inferred from RM maps are a possible probe for the cosmic-ray content of a given galaxy. Our calculations highlight the importance of cosmic rays in these measures, making them an essential ingredient of realistic models of the interstellar medium.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Bayesian Optimization Framework for Imperfect Data or Models

Conventional Bayesian optimization methods implicitly assume that the data and model being optimized are “perfect.” This assumption leads to inaccurate posterior probability distribution functions (PDFs) when applied to “imperfect” data or models. The new Bayesian optimization framework presented in this report provides a way to parameterize the effect of imperfections usually encountered in a prior PDF of generalized data or a model on the posterior PDF. The effects of imperfections are parameterized by a set of constraints imposed on the posterior expectation values of deviations between the data and the model and on their covariance matrix elements. A particular set of values for these constraints conveys an evaluator’s best estimate of the effect of imperfections on the corresponding posterior expectation values. When a prior PDF of generalized data is assumed to be normal, an expression for a posterior PDF satisfying an arbitrary set of constraints is derived analytically for linear models. An analogous iterative algorithm is given for nonlinear models. The corresponding posterior PDF should be used to estimate any posterior expectation values in the presence of imperfections parameterized by that set of constraints. A posterior PDF of a conventional Bayesian optimization method is recovered analytically when all evaluator-specified constraints are set to zero (i.e., in the absence of any imperfections). The analytical expressions derived in this report for normal PDFs and linear models were verified numerically by a Metropolis–Hastings Monte Carlo method. The methods presented herein could be applied to any kind of data or models, including differential cross-section data or integral benchmark experiments.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1989

An accurate analytic approximation to the non-linear change in volume of solids with applied pressure

An accurate analytic expression for the nonlinear change of the volume of a solid as a function of applied pressure is of great interest in high-pressure experimentation. It is found that a two-parameter analytic expression, fits the experimental volume-change data to within a few percent over the entire experimentally attainable pressure range. Results are presented for 24 different materials including metals, ceramic semiconductors, polymers, and ionic and rare-gas solids.

Schlosser, Herbert↗

DOE OSTI2011

Constraining warm dark matter with cosmic shear power spectra

We investigate potential constraints from cosmic shear on the dark matter particle mass, assuming all dark matter is made up of light thermal relic particles. Given the theoretical uncertainties involved in making cosmological predictions in such warm dark matter scenarios we use analytical fits to linear warm dark matter power spectra and compare (i) the halo model using a mass function evaluated from these linear power spectra and (ii) an analytical fit to the non-linear evolution of the linear power spectra. We optimistically ignore the competing effect of baryons for this work. We find approach (ii) to be conservative compared to approach (i). We evaluate cosmological constraints using these methods, marginalising over four other cosmological parameters. Using the more conservative method we find that a Euclid-like weak lensing survey together with constraints from the Planck cosmic microwave background mission primary anisotropies could achieve a lower limit on the particle mass of 2.5 keV.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1991

A methodology for using nonlinear aerodynamics in aeroservoelastic analysis and design

A methodology is presented for using the Volterra-Wiener theory of nonlinear systems in aeroservoelastic (ASE) analyses and design. The theory is applied to the development of nonlinear aerodynamic response models that can be defined in state-space form and are, therefore, appropriate for use in modern control theory. The theory relies on the identification of nonlinear kernels that can be used to predict the response of a nonlinear system due to an arbitrary input. A numerical kernel identification technique, based on unit impulse responses, is presented and applied to a simple bilinear, single-input-single-output system. The linear kernel (unit impulse response) and the nonlinear second-order kernel of the system are numerically-identified and compared with the exact, analytically-defined linear and second-order kernels. This kernel identification technique is then applied to the CAP-TSD code for identification of the linear and second-order kernels of a NACA64A010 rectangular wing undergoing pitch at M = 0.5, M = 0.85 (transonic), and M = 0.93 (transonic). Results presented demonstrate the feasibility of this approach for use with nonlinear, unsteady aerodynamic responses.

Silva, Walter A.↗

DOE OSTI2011

Magnetic field gradient effects on Rayleigh-Taylor instability with continuous magnetic field and density profiles

In this paper, the effects of magnetic field gradient (i.e., the magnetic field transition layer effects) on the Rayleigh-Taylor instability (RTI) with continuous magnetic field and density profiles are investigated analytically. The transition layers of magnetic field and density with two different typical profiles are studied and the analytic expressions of the linear growth rate of the RTI are obtained. It is found that the magnetic field effects strongly reduce the linear growth rate of the RTI, especially when the perturbation wavelength is short. The linear growth rate of the RTI increases with the thickness of the magnetic field transition layer, especially for the case of small thickness of the magnetic field transition layer. When the magnetic field transition layer width is long enough, the linear growth rate of the RTI can be saturated. Thus when one increases the width of the magnetic field transition layer, the linear growth rate of the RTI increases only in a certain range, which depends on the magnetic field strength. The numerical results are compared with the analytic linear growth rates and they agree well with each other.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Three-dimensional structures of equatorial waves and the resulting super-rotation in the atmosphere of a tidally locked hot Jupiter

Three-dimensional (3D) equatorial trapped waves excited by stellar isolation and the resulting equatorial super-rotating jet in a vertical stratified atmosphere of a tidally locked hot Jupiter are investigated. Taking the hot Jupiter HD 189733b as a fiducial example, we analytically solve linear equations subject to stationary stellar heating with a uniform zonal-mean flow included. We also extract wave information in the final equilibrium state of the atmosphere from our radiative hydrodynamical simulation for HD 189733b. Our analytic wave solutions are able to qualitatively explain the 3D simulation results. Apart from previous wave studies, investigating the vertical structure of waves allows us to explore new wave features such as the wavefronts tilts related to the Rossby-wave resonance as well as dispersive equatorial waves. We also attempt to apply our linear wave analysis to explain some numerical features associated with the equatorial jet development seen in the general circulation model by Showman and Polvani. During the spin-up phase of the equatorial jet, the acceleration of the jet can be in principle boosted by the Rossby-wave resonance. However, we also find that as the jet speed increases, the Rossby-wave structure shifts eastward, while the Kelvin-wave structure remains approximately stationary, leading to the decline of the acceleration rate. Our analytic model of jet evolution implies that there exists only one stable equilibrium state of the atmosphere, possibly implying that the final state of the atmosphere is independent of initial conditions in the linear regime. Limitations of our linear model and future improvements are also discussed.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

The Spectrum of Thermally Stimulated Surface Plasmon Polaritons of a Linear Sample

An analytical model of the spectrum of thermally stimulated surface plasmon polaritons (TSSPPs) coming to the edge of a linear conducting sample has been developed. It has been found that the spectrum of such TSSPPs obeys neither the Wien law nor the Stefan–Boltzmann law for thermal radiation. The maximum of this spectrum is shifted to the low-frequency region with respect to the spectrum of the absolutely black body, and the magnitude of the shift is proportional to the sample length. The plasmon nature of the intensity increment of thermal radiation from the edge of a plane face of a duralumin sample has been verified experimentally. It has been shown that the intensity and spectrum of this increment can be controlled both by the sample temperature and by the extension of the face.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2006

Analytical and Numerical Results for an Adhesively Bonded Joint Subjected to Pure Bending

A one-dimensional, semi-analytical methodology that was previously developed for evaluating adhesively bonded joints composed of anisotropic adherends and adhesives that exhibit inelastic material behavior is further verified in the present paper. A summary of the first-order differential equations and applied joint loading used to determine the adhesive response from the methodology are also presented. The method was previously verified against a variety of single-lap joint configurations from the literature that subjected the joints to cases of axial tension and pure bending. Using the same joint configuration and applied bending load presented in a study by Yang, the finite element analysis software ABAQUS was used to further verify the semi-analytical method. Linear static ABAQUS results are presented for two models, one with a coarse and one with a fine element meshing, that were used to verify convergence of the finite element analyses. Close agreement between the finite element results and the semi-analytical methodology were determined for both the shear and normal stress responses of the adhesive bondline. Thus, the semi-analytical methodology was successfully verified using the ABAQUS finite element software and a single-lap joint configuration subjected to pure bending.

Smeltzer, Stanley S., III↗

DOE OSTI2012

A Hydro-mechanical Model and Analytical Solutions for Geomechanical Modeling of Carbon Dioxide Geological Sequestration

We present a hydro-mechanical model for geological sequestration of carbon dioxide. The model considers the poroelastic effects by taking into account the coupling between the geomechanical response and the fluid flow in greater detail. The simplified hydro-mechanical model includes the geomechanical part that relies on the linear elasticity, while the fluid flow is based on the Darcy’s law. Two parts were coupled using the standard linear poroelasticity. Analytical solutions for pressure field were obtained for a typical geological sequestration scenario. The model predicts the temporal and spatial variation of pressure field and effects of permeability and elastic modulus of formation on the fluid pressure distribution.

sequestration, geomechanics, Multi-scale, poro-ela↗

DOE OSTI2012

Longitudinal singular response of dusty plasma medium in weak and strong coupling limits

The longitudinal response of a dusty plasma medium in both weak and strong coupling limits has been investigated in detail using analytic as well as numerical techniques. In particular, studies on singular response of the medium have been specifically investigated here. A proper Galilean invariant form of the generalized hydrodynamic fluid model has been adopted for the description of the dusty plasma medium. For weak non-linear response, analytic reductive perturbative approach has been adopted. It is well known that in the weak coupling regime for the dusty plasma medium, such an analysis leads to the Korteweg-de Vries equation (KdV) equation and predicts the existence of localized smooth soliton solutions. We show that the strongly coupled dust fluid with the correct Galilean invariant form does not follow the KdV paradigm. Instead, it reduces to the form of Hunter-Saxton equation, which does not permit soliton solutions. The system in this case displays singular response with both conservative as well as dissipative attributes. At arbitrary high amplitudes, the existence and spontaneous formation of sharply peaked cusp structures in both weak and strong coupling regimes has been demonstrated numerically.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Stochastic linear multistep methods for the simulation of chemical kinetics

In this paper, we introduce the Stochastic Adams-Bashforth (SAB) and Stochastic Adams-Moulton (SAM) methods as an extension of the τ-leaping framework to past information. Using the Θ-trapezoidal τ-leap method of weak order two as a starting procedure, we show that the k-step SAB method with k ≥ 3 is order three in the mean and correlation, while a predictor-corrector implementation of the SAM method is weak order three in the mean but only order one in the correlation. These convergence results have been derived analytically for linear problems and successfully tested numerically for both linear and non-linear systems. A series of additional examples have been implemented in order to demonstrate the efficacy of this approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Temperature-dependent changes in gas chromatographic separation metrics for trihexyl(tetradecyl)phosphonium-based ionic liquid stationary phases and comparison to conventional polysiloxane stationary phases

Here, to assess whether the trihexyl(tetradecyl)phosphonium chloride ([P 66614 + ][Cl - ]) ionic liquid (IL), employed as a gas chromatographic stationary phase, exhibits temperature-dependent phase transitions or structural heterogeneity, retention thermodynamics for probe molecules of varied chemical structure were investigated by gas chromatography (GC) over the temperature range of 25 to 64 °C using van’t Hoff analysis. All van’t Hoff plots for n-alkanes (C8–C12) and other probe analytes were linear, indicating the absence of detectable phase-transition behavior. The [P 66614 + ][Cl - ] IL was further compared with the [P 66614 + ] bis[(trifluoromethyl)sulfonyl]imide ([P 66614 + ][NTf 2 - ]) IL and commercial polysiloxane stationary phases in terms of temperature-dependent resolution behavior and chromatographic selectivity over the temperature range of 28–52 °C. The resolution factors of analytes in mixtures obtained using gas chromatography–mass spectrometry (GC–MS) and the summation of resolution values decreased smoothly with temperature on both IL stationary phases and on the dimethylphenylcyano-substituted polymeric stationary phase (OV-1701), whereas the poly(50% diphenyl/50% dimethyl siloxane) stationary phase (SPB-50) exhibited irregularities in its temperature-dependent summation of resolution profile, showing a distinct maximum in the temperature range of 34–40 °C. Selectivity values for the IL stationary phases were largely determined by the anion, with the [P 66614 + ][Cl - ] IL providing enhanced separation between polar and aromatic analytes, while the [P 66614 + ][NTf 2 - ] IL favored dispersive and π-π interactions that resulted in a reversal of elution order for some aliphatic–aromatic and alkyne-containing analyte pairs. Capillary columns prepared using different surface activation methods and coated with identical [P 66614 + ][Cl - ] IL stationary phase showed indistinguishable temperature-dependent trends in summation of resolution value and selectivity. An evaluation of analyte-specific selectivity provides insight into the characteristic separation behavior of the stationary phases and enables identification of analyte classes that are more efficiently separated on the [P 66614 + ]-based IL stationary phases compared to conventional stationary phase materials.

Chromatographic selectivity↗

DOE OSTI2018

Derived Optimal Linear Combination Evapotranspiration (DOLCE): a global gridded synthesis ET estimate

Accurate global gridded estimates of evapotranspiration (ET) are key to understanding water and energy budgets, in addition to being required for model evaluation. Several gridded ET products have already been developed which differ in their data requirements, the approaches used to derive them and their estimates, yet it is not clear which provides the most reliable estimates. This paper presents a new global ET dataset and associated uncertainty with monthly temporal resolution for 2000–2009. Six existing gridded ET products are combined using a weighting approach trained by observational datasets from 159 FLUXNET sites. The weighting method is based on a technique that provides an analytically optimal linear combination of ET products compared to site data and accounts for both the performance differences and error covariance between the participating ET products. We examine the performance of the weighting approach in several in-sample and out-of-sample tests that confirm that point-based estimates of flux towers provide information on the grid scale of these products. We also provide evidence that the weighted product performs better than its six constituent ET product members in four common metrics. Uncertainty in the ET estimate is derived by rescaling the spread of participating ET products so that their spread reflects the ability of the weighted mean estimate to match flux tower data. While issues in observational data and any common biases in participating ET datasets are limitations to the success of this approach, future datasets can easily be incorporated and enhance the derived product.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2016

A Novel Centrality Measure for Network-wide Cyber Vulnerability Assessment

In this work we propose a novel formulation that models the attack and compromise on a cyber network as a combination of two parts - direct compromise of a host and the compromise occurring through the spread of the attack on the network from a compromised host. The model parameters for the nodes are a concise representation of the host profiles that can include the risky behaviors of the associated human users while the model parameters for the edges are based on the existence of vulnerabilities between each pair of connected hosts. The edge models relate to the summary representations of the corresponding attack-graphs. This results in a formulation based on Random Walk with Restart (RWR) and the resulting centrality metric can be solved for in an efficient manner through the use of sparse linear solvers. Thus the formulation goes beyond mere topological considerations in centrality computations by summarizing the host profiles and the attack graphs into the model parameters. The computational efficiency of the method also allows us to also quantify the uncertainty in the centrality measure through Monte Carlo analysis.

Centrality↗

DOE OSTI2018

Easy, Fast, and Reproducible Quantification of Cholesterol and Other Lipids in Human Plasma by Combined High Resolution MSX and FTMS Analysis

Reliable, cost-effective, and gold-standard absolute quantification of non-esterified cholesterol in human plasma is of paramount importance in clinical lipidomics and for the monitoring of metabolic health. Here, we compared the performance of three mass spectrometric approaches available for direct detection and quantification of cholesterol in extracts of human plasma. These approaches are high resolution full scan Fourier transform mass spectrometry (FTMS) analysis, parallel reaction monitoring (PRM), and novel multiplexed MS/MS (MSX) technology, where fragments from selected precursor ions are detected simultaneously. Evaluating the performance of these approaches in terms of dynamic quantification range, linearity, and analytical precision showed that the MSX-based approach is superior to that of the FTMS and PRM-based approaches. To further show the efficacy of this approach, we devised a simple routine for extensive plasma lipidome characterization using only 8 μL of plasma, using a new commercially available ready-to-spike-in mixture with 14 synthetic lipid standards, and executing a single 6 min sample injection with combined MSX analysis for cholesterol quantification and FTMS analysis for quantification of sterol esters, glycerolipids, glycerophospholipids, and sphingolipids. Using this simple routine afforded reproducible and absolute quantification of 200 lipid species encompassing 13 lipid classes in human plasma samples. Notably, the analysis time of this procedure can be shortened for high throughput-oriented clinical lipidomics studies or extended with more advanced MS{sup ALL} technology (Almeida R. et al., J. Am. Soc. Mass Spectrom. 26, 133–148 [1]) to support in-depth structural elucidation of lipid molecules. .

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

The Three Hundred Project: Modeling baryon and hot-gas fraction evolution in simulated clusters

The baryon fraction of galaxy clusters, expressed as the ratio between the mass in baryons (including both stars and cold or hot gas) and the total mass, is a powerful tool to provide information on the cosmological parameters, while the hot-gas fraction provides indications on the physics of the intracluster plasma and its interplay with the processes that drive galaxy formation. Using cosmological hydrodynamical simulations of about 300 simulated massive galaxy clusters with a median mass M 500 ≈ 7 × 10 14 M ⊙ at z = 0, we model the relations between total mass and either baryon fraction or the hot gas fractions at overdensities Δ = 2500, 500, and 200 with respect to the cosmic critical density, and their evolution from z ∼ 0 to z ∼ 1.3. We utilized the simulated galaxy clusters from the Three Hundred project, which include star formation and feedback from both supernovae and active galactic nuclei. We fit the simulation results for such scaling relations against three analytic forms (linear, quadratic, and logarithmic in a logarithmic plane) and three forms for the redshift dependence, and we considered as a variable both the inverse of the cosmic scale factor, (1 + z), and the Hubble expansion rate, E(z). We show that power-law dependencies on cluster mass poorly describe the investigated relations. A power law fails to simultaneously capture the flattening of the total baryon and gas fractions at high masses, their drop at low masses, and the transition between these two regimes. The other two functional forms provide a more accurate description of the curvature in mass scaling. The fractions measured within smaller radii exhibit a stronger evolution than those measured within larger radii. From the analysis of these simulations, we evince that as long as we include systems in the mass range herein investigated, the baryon or gas fraction can be accurately related to the total mass through either a parabola or a logarithm in the logarithmic plane. The trends are common to all modern hydro simulations, although the amplitude of the drop at low masses might differ. Being able to observationally determine the gas fraction in groups will thus provide constraints on the baryonic physics.

galaxy clusters↗

DOE OSTI2015

Steady state likelihood ratio sensitivity analysis for stiff kinetic Monte Carlo simulations

Kinetic Monte Carlo simulation is an integral tool in the study of complex physical phenomena present in applications ranging from heterogeneous catalysis to biological systems to crystal growth and atmospheric sciences. Sensitivity analysis is useful for identifying important parameters and rate-determining steps, but the finite-difference application of sensitivity analysis is computationally demanding. Techniques based on the likelihood ratio method reduce the computational cost of sensitivity analysis by obtaining all gradient information in a single run. However, we show that disparity in time scales of microscopic events, which is ubiquitous in real systems, introduces drastic statistical noise into derivative estimates for parameters affecting the fast events. In this work, the steady-state likelihood ratio sensitivity analysis is extended to singularly perturbed systems by invoking partial equilibration for fast reactions, that is, by working on the fast and slow manifolds of the chemistry. Derivatives on each time scale are computed independently and combined to the desired sensitivity coefficients to considerably reduce the noise in derivative estimates for stiff systems. The approach is demonstrated in an analytically solvable linear system.

Núñez, M.↗