Development of an Analytical Optical Method for Linear Fresnel Collectors
Abstract not provided
14 SOLAR ENERGY↗
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Results for “Analytic linearization”
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.
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Constraining cosmological parameters with needlet internal linear combination maps. I. Analytic power spectrum formalism
Not provided.
Astronomy & Astrophysics↗
Asynchrony in Task-Parallel Linear Algebra Based Graph Analytics.
Abstract not provided.
Wolf, Michael↗
Second Linear Response Theory and the Analytic Calculation of Excited-State Properties
We present a method based on second linear response time-dependent density func- tional theory (TDDFT) to calculate permanent and transition multipoles of excited states, which are required to compute excited-state absorption/emission spectra, multi- photon optical processes, among others. In previous work, we examined computations based on second linear response theory in which linear response TDDFT was employed twice. In contrast, the present methodology only requires information from a single linear response calculation to compute the excited-state properties. These are eval- uated analytically through various algebraic operations involving electron repulsion integrals and excitation vectors. The present derivation focuses on full many-body wave functions instead of single orbitals, as in our previous approach. Here, we test the proposed method by applying it to several diatomic and triatomic molecules. This shows that the computed excited-state dipoles are consistent with respect to reference equation-of-motion coupled cluster calculations.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Exact analytic solution for non-linear density fluctuation in a ΛCDM universe
We derive the exact third-order analytic solution of the matter density fluctuation in the proper-time hypersurface in a ΛCDM universe, accounting for the explicit time-dependence and clarifying the relation to the initial condition. Furthermore, we compare our analytic solution to the previous calculation in the comoving gauge, and to the standard Newtonian perturbation theory by providing Fourier kernels for the relativistic effects. Our results provide an essential ingredient for a complete description of galaxy bias in the relativistic context.
79 ASTRONOMY AND ASTROPHYSICS↗
Stabilization of electron-scale turbulence by electron density gradient in national spherical torus experiment
Theory and experiments have shown that electron temperature gradient (ETG) turbulence on the electron gyro-scale, k{sub ⊥}ρ{sub e} ≲ 1, can be responsible for anomalous electron thermal transport in NSTX. Electron scale (high-k) turbulence is diagnosed in NSTX with a high-k microwave scattering system [D. R. Smith et al., Rev. Sci. Instrum. 79, 123501 (2008)]. Here we report on stabilization effects of the electron density gradient on electron-scale density fluctuations in a set of neutral beam injection heated H-mode plasmas. We found that the absence of high-k density fluctuations from measurements is correlated with large equilibrium density gradient, which is shown to be consistent with linear stabilization of ETG modes due to the density gradient using the analytical ETG linear threshold in F. Jenko et al. [Phys. Plasmas 8, 4096 (2001)] and linear gyrokinetic simulations with GS2 [M. Kotschenreuther et al., Comput. Phys. Commun. 88, 128 (1995)]. We also found that the observed power of electron-scale turbulence (when it exists) is anti-correlated with the equilibrium density gradient, suggesting density gradient as a nonlinear stabilizing mechanism. Higher density gradients give rise to lower values of the plasma frame frequency, calculated based on the Doppler shift of the measured density fluctuations. Linear gyrokinetic simulations show that higher values of the electron density gradient reduce the value of the real frequency, in agreement with experimental observation. Nonlinear electron-scale gyrokinetic simulations show that high electron density gradient reduces electron heat flux and stiffness, and increases the ETG nonlinear threshold, consistent with experimental observations.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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↗
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↗
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↗
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↗
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↗
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↗
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↗
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↗
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↗
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↗
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↗
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↗