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At least 271 records · Page 15

Formation of a rotational accretion column

We consider the problem of the flow produced by the accretion of gas from a rotating cloud onto a point gravitational source. It is shown that, for a cloud initially in uniform rotation, the effect of accretion is to produce a Taylor column in the cloud parallel to the rotation axis. Only gas within the column is accreted; the gas outside the column undergoes oscillatory flow, which is probably subject to shear instability. The column forms in approximately one-half rotation period from the time at which accretion begins. Its initial radius is determined by the accretion rate and the angular velocity of the cloud. Application of the results to the formation of Jupiter by accretion is discussed.

Cassen, P.↗

Full CI benchmark calculations on CH3

Full CI calculations have been performed on the CH3 radical. The full CI results are compared to those obtained using CASSCF/multireference CI and coupled-pair functional methods, both at the equilibrium CH distance and at geometries with the three CH bonds extended. In general, the performance of the approximate methods is similar to that observed in calculations on other molecules in which one or two bonds were stretched.

Bauschlicher, Charles W., Jr.↗

Efficient manifolds tracing for planar maps

Here, we present an exact calculation method and an approximation technique for tracing the invariant manifolds of unstable periodic orbits of planar maps. The exact approach relies on an adaptive refinement procedure that prevents redundant calculations occurring in other approaches, and the approximated method relies on a novel interpolation approach based on normal displacement functions. The resulting approximated manifold is precise when compared to the exact one, and its relative computational cost falls like the inverse of the manifold length. To present the tracing method, we obtain the invariant manifolds of the Chirikov-Taylor map, and as an application we illustrate the transition from homoclinic to heteroclinic chaos in the Duffing oscillator that leads from localized chaos to global chaotic motion.

74 ATOMIC AND MOLECULAR PHYSICS↗

Modeling material interfaces with hybrid adhesion method

A molecular dynamics simulation approach is presented to approximate layered material structures using discrete interatomic potentials through classical mechanics and the underlying principles of quantum mechanics. This method isolates the energetic contributions of the system into two pure material layers and an interfacial region used to simulate the adhesive properties of the diffused interface. The strength relationship of the adhesion contribution is calculated through small-scale separation calculations and applied to the molecular surfaces through an inter-layer bond criterion. By segregating the contributions into three regions and accounting for the interfacial excess energies through the adhesive surface bonds, it is possible to model each material with an independent potential while maintaining an acceptable level of accuracy in the calculation of mechanical properties. This method is intended for the atomistic study of the delamination mechanics, typically observed in thin-film applications. Therefore, the work presented in this paper focuses on mechanical tensile behaviors, with observations in the elastic modulus and the delamination failure mode. To introduce the hybrid adhesion method, we apply the approach to an ideal bulk copper sample, where an interface is created by disassociating the force potential in the middle of the structure. Various mechanical behaviors are compared to a standard EAM control model to demonstrate the adequacy of this approach in a simple setting. In addition, we demonstrate the robustness of this approach by applying it on (1) a Cu-Cu 2 O interface with interactions between two atom types, and (2) an Al-Cu interface with two dissimilar FCC lattices. These additional examples are verified against EAM and COMB control models to demonstrate the accurate simulation of failure through delamination, and the formation and propagation of dislocations under loads. Finally, the results conclude that by modeling the energy contributions of an interface using hybrid adhesion bonds, we can provide an accurate approximation method for studies of large-scale mechanical properties, as well as the representation of various delamination phenomena at the atomic scale.

36 MATERIALS SCIENCE↗

The QPO in RE J1034+396 Originates in the Hot Corona

RE J1034+396 is one of the few active galactic nuclei (AGNs) with a significant quasiperiodic oscillation (QPO). The QPO has been observed in over 1 Ms of XMM-Newton observations spanning over a decade. We investigate the power spectral density function (PSD) of seven long (∼90 ks) XMM-Newton observations of the AGN RE J1034+396 in two energy bands. The soft (0.3–0.5 keV) band targets emission from the disk, while the hard (2–7 keV) band isolates the primary X-ray continuum emission from the corona. The QPO is significantly detected in the hard band of five of the seven observations. The best-fitting models indicate that the QPO detection in both bands is entirely attributable to the coronal emission with no additional contribution from the disk. This explains the strong coherence between the hard and soft bands at the QPO frequency. The covariance spectrum is consistent with this picture as the variability at QPO frequencies is attributed solely to fluctuations in the hot corona. The time lag as a function of energy is well described by a ∼2000 s intrinsic soft lag, resulting from the disk responding to emission from the corona, that undergoes phase wrapping at approximately the QPO frequency. By demonstrating that in this system the QPO arises in the corona, we provide new insights into the mechanisms generating QPOs.

Active galactic nuclei↗

Coarse-grained basalt 71597 - A product of partial olivine accumulation

Rock 71597, a coarse-grained plagioclase-poikilitic basalt that contains 15.8% MgO and 19.3% modal olivine, is described. Olivine and ilmenite crystals occur in two size generations, and large subequant olivine crystals, small 'matrix' olivines, and large ilmenite crystals are characterized. Since large olivine and ilmenite crystals with skeletal habits suggestive of crystallization under relatively rapid cooling are found in a rock whose texture is consonant with slower cooling, it is suggested that the large skeletal crystals formed toward the more rapidly cooled margin of a flow and accumulated by gravitational crystal settling toward the flow's interior. In support of this hypothesis, calculations indicate that the observed olivine compositions are approximately 10 mol% too Fe-rich to have crystallized from a melt of composition corresponding to that of 71597.

Warner, R. D.↗

Approach for Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1-D Euler CFD (computational fluid dynamics) code. Given uncertainties in statistically independent, random, normally distributed input variables, a first- and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Putko, Michele M.↗

Taylor wave solution for a general equation of state

This document describes a solution procedure for calculating the Taylor wave behind an unsupported Chapman–Jouguet (CJ) detonation in planar, cylindrical, and spherical geometries given a general equation of state. The resulting semi-analytic solution can be utilized to examine new equation of state models for detonation products and during the verification of hydrodynamic codes. The governing partial differential equations are reduced to ordinary differential equations in both characteristic and self-similar forms. The first-order systems corresponding to each geometry are amenable to solution numerically using commonly available methods. A difficulty arises at the CJ point in radial coordinates where the similarity equations become singular. Two separate strategies are proposed to integrate the first-order system. The first one uses an asymptotic approximation near the CJ point that can be used to perturb the boundary conditions. The second one applies a change of variables which removes the singularity at the expense of an additional equation to be integrated. A test problem is provided for the Davis products equation of state to illustrate the qualitative features of the Taylor wave in each geometric configuration and compared with a Lagrangian hydrodynamics research code. A Python code listing gives an implementation using the SciPy library to assists users in generating the results.

97 MATHEMATICS AND COMPUTING↗

Characterizing the modulation transfer function for X-ray radiography in high energy density experiments

Here, the Modulation Transfer Function ( MTF ) is an established means for characterizing imaging performance of X-ray radiography systems. We report on experiments using high energy, laser-driven X-ray radiography systems that assess performance using MTF values measured with the knife-edge projection method. The broadband, hard X-ray systems under study use line-projection imaging produced by narrowing the laser-generated X-ray source with a slit. We find that good contrast resolution can be achieved (the MTF = 0.5 at 75 μm wavelength) and that this performance is reproduced on different laser facilities. We also find that the MTF is sensitive both to the thickness of the line-projection slit and to the backing material thickness under the knife-edge. Both these sensitivities are due to a common mechanism, namely induced changes in the spectrally-averaged spatial widths of the X-ray source. The same line-projection system is also used on experimental campaigns measuring Rayleigh-Taylor instability growth by dynamically imaging sinusoidal, high Z micro-targets with wavelengths of 100 μm or less. By applying the measured MTF values to correct the ripple target contrast measurements, we can predict ripple growth to approximately 10% accuracy.

47 OTHER INSTRUMENTATION↗

Mixing with applications to inertial-confinement-fusion implosions

Approximate one-dimensional (1D) as well as 2D and 3D simulations are playing an important supporting role in the design and analysis of future experiments at National Ignition Facility. This work is mainly concerned with 1D simulations, used extensively in design and optimization. We couple a 1D buoyancy-drag mix model for the mixing zone edges with a 1D inertial confinement fusion simulation code. This analysis predicts that National Ignition Campaign (NIC) designs are located close to a performance cliff, so modeling errors, design features (fill tube and tent) and additional, unmodeled instabilities could lead to significant levels of mix. The performance cliff we identify is associated with multimode plastic ablator (CH) mix into the hot-spot deuterium and tritium (DT). The buoyancy-drag mix model is mode number independent and selects implicitly a range of maximum growth modes. Our main conclusion is that single effect instabilities are predicted not to lead to hot-spot mix, while combined mode mixing effects are predicted to affect hot-spot thermodynamics and possibly hot-spot mix. Combined with the stagnation Rayleigh-Taylor instability, we find the potential for mix effects in combination with the ice-to-gas DT boundary, numerical effects of Eulerian species CH concentration diffusion, and ablation-driven instabilities. With the help of a convenient package of plasma transport parameters developed here, we give an approximate determination of these quantities in the regime relevant to the NIC experiments, while ruling out a variety of mix possibilities. Plasma transport parameters affect the 1D buoyancy-drag mix model primarily through its phenomenological drag coefficient as well as the 1D hydro model to which the buoyancy-drag equation is coupled.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

On the Lighthill relationship and sound generation from isotropic turbulence

In 1952, Lighthill developed a theory for determining the sound generated by a turbulent motion of a fluid. With some statistical assumptions, Proudman applied this theory to estimate the acoustic power of isotropic turbulence. Recently, Lighthill established a simple relationship that relates the fourth-order retarded time and space covariance of his stress tensor to the corresponding second-order covariance and the turbulent flatness factor, without making statistical assumptions for a homogeneous turbulence. Lilley revisited Proudman's work and applied the Lighthill relationship to evaluate directly the radiated acoustic power from isotropic turbulence. After choosing the time separation dependence in the two-point velocity time and space covariance based on the insights gained from direct numerical simulations, Lilley concluded that the Proudman constant is determined by the turbulent flatness factor and the second-order spatial velocity covariance. In order to estimate the Proudman constant at high Reynolds numbers, we analyzed a unique data set of measurements in a large wind tunnel and atmospheric surface layer that covers a range of the Taylor microscale based on Reynolds numbers 2.0 x 10(exp 3) less than or equal to R(sub lambda) less than or equal to 12.7 x 10(exp 3). Our measurements demonstrate that the Lighthill relationship is a good approximation, providing additional support to Lilley's approach. The flatness factor is found between 2.7 - 3.3 and the second order spatial velocity covariance is obtained. Based on these experimental data, the Proudman constant is estimated to be 0.68 - 3.68.

Zhou, YE↗

Helium abundances on the moon: Assumptions and estimates

Nuclear energy is a highly desirable source of energy, and He-3 is the most prized of the fusion reactants. As the Wisconsin Group has emphasized, He-3 may be the only true economic ore on the Moon. The lack of a shielding atmosphere on the Moon permits solar-wind alpha particles to impinge upon the lunar regolith and become implanted into the various solid components. In particular, large quantities of helium (5 to 50 ppm) are presented. The measured parameter of I(sub s)/FeO, a direct indicator of maturity and exposure age, can be used as a first approximation to predict the abundances of many solar-wind components in the soils. However, because ilmenite has a much higher retentivity for helium than the other phases, the TiO2 contents of the soils are better indicators of helium contents (Taylor, Space 90). High-Ti mare bassalt regions, such as at the Apollo 17 locale, appear to be the best areas for He mining (15 to 50 ppm He(sub T)), versus 3 to 9 ppm in the Highlands. However, the relationships between I(sub s)/FeO, TiO2 and He-3 contents are complicated - e.g., many of the most He-rich soils are immature to submature. The amount of He-3 in the regolith of the moon is estimated at 220,000 tons in the outer 2 m of the Maria.

Taylor, Lawrence A.↗

An approach to the development of numerical algorithms for first order linear hyperbolic systems in multiple space dimensions: The constant coefficient case

Two methods for developing high order single step explicit algorithms on symmetric stencils with data on only one time level are presented. Examples are given for the convection and linearized Euler equations with up to the eighth order accuracy in both space and time in one space dimension, and up to the sixth in two space dimensions. The method of characteristics is generalized to nondiagonalizable hyperbolic systems by using exact local polynominal solutions of the system, and the resulting exact propagator methods automatically incorporate the correct multidimensional wave propagation dynamics. Multivariate Taylor or Cauchy-Kowaleskaya expansions are also used to develop algorithms. Both of these methods can be applied to obtain algorithms of arbitrarily high order for hyperbolic systems in multiple space dimensions. Cross derivatives are included in the local approximations used to develop the algorithms in this paper in order to obtain high order accuracy, and improved isotropy and stability. Efficiency in meeting global error bounds is an important criterion for evaluating algorithms, and the higher order algorithms are shown to be up to several orders of magnitude more efficient even though they are more complex. Stable high order boundary conditions for the linearized Euler equations are developed in one space dimension, and demonstrated in two space dimensions.

Goodrich, John W.↗

Higher-Order Approximations for Stabilizing Zero-Energy Modes in Peridynamics Crystal Plasticity Models with Large Horizon Interactions

The non-ordinary state-based peridynamics theory combines non-local dynamic techniques with a desirable correspondence material principle, allowing for the use of continuum mechanics constitutive models. Such an approach presents a unique capability for solving problems involving discontinuities (e.g., strain localization, fracture, and fragmentation). However, the correspondence-based peridynamics models often suffer from zero-energy mode instabilities in numerical implementation, primarily due to the approximations of the non-local deformation gradient tensor. This paper focuses on a computational scheme for eliminating the zero-energy mode oscillations using a choice of influence functions that improve the truncation error in a higher-order Taylor series expansion of the deformation gradient. The novelty here is a tensor-based derivation of the linear constraint equations, which can be used to systematically identify the particle interaction weight functions for various user-specified horizon radii. In this paper, the proposed higher-order stabilization scheme is demonstrated for multi-dimensional examples involving polycrystalline and composite microstructures, along with comparisons against conventional finite element methods. The proposed stabilization scheme is shown to be highly effective in suppressing the spurious zero-energy mode oscillations in all numerical examples while enabling efficient simulations of strain localizations across material interfaces.

Non-Ordinary State-Based Peridynamics↗

An efficient method for estimating neighboring steady-state numerical solutions to the Euler equations

The paper concentrates on a linear approximation method for predicting the changes occurring in steady-state numerical solutions of the Euler equations as a consequence of small changes in the independent variables which control the problem. The importance of proper boundary-condition treatment and other issues concerning the problem are covered along with the importance of proper algorithm selection for a fully supersonic inviscid flow. The method is applied to a subsonic nozzle involving variation of the pressure on the outflow boundary and to a supersonic inlet involving variation of the inflow Mach number. In the subsonic test case, the comparisons between the predicted and conventional numerical solutions are shown to be good, while in the supersonic test case, the agreement between the approximation method and conventional numerical solution starts out well but rapidly degenerates at some point in the flowfield as the perturbation of the boundary conditions is increased.

Taylor, Arthur C., III↗

Theoretical study of various nonlinear phenomena in plasma systems and scaling of magneto-inertial-fusion targets

Plasma physics is an exciting field of study with a wide variety of nonlinear processes that come into play. Examples of such processes include the interaction of small-scale turbulence with large-scale plasma structures and the nonlinear saturation of plasma instabilities, for example those of magneto-hydrodynamical nature. During this Truman LDRD project, I studied a collection of nonlinear problems that are of interest to the field of plasma physics. This LDRD report summarizes four main research accomplishments. First, a new statistical model for describing inhomogeneous drift-wave turbulence inter- acting with zonal flows was developed. This new model includes the effects of nonlinear wave-wave collisions, which are expected to change the spectrum of the underlying DW turbulence and therefore the generation of zonal flows. Second, a new mathematical formalism was proposed to systematically apply the non- linear WKB approximation to general field theories, including those often used in fluid dynamics. This formalism represents an interesting tool for studying physical systems that show an explicit scale separation. Third, a weakly nonlinear model was developed to describe the magneto-Rayleigh-Taylor instability. This instability is of paramount importance to understand as it can reduce the performance of magnetic-inertial-fusion (MIF) platforms. The developed models captures the effects of harmonic generation and saturation of the linear growth of the instability. Finally, a framework was proposed for scaling magneto-inertial fusion (MIF) targets to larger pulsed-power drivers. From this framework, a set of scaling rules were derived that conserve the physical regimes of MIF systems when scaling up in peak current. By doing so, deleterious nonlinear processes that affect MIF performance may be kept at bay.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Validity of Five Satellite-Based Latent Heat Flux Algorithms for Semi-arid Ecosystems

Accurate estimation of latent heat flux (LE) is critical in characterizing semiarid ecosystems. Many LE algorithms have been developed during the past few decades. However, the algorithms have not been directly compared, particularly over global semiarid ecosystems. In this paper, we evaluated the performance of five LE models over semiarid ecosystems such as grassland, shrub, and savanna using the Fluxnet dataset of 68 eddy covariance (EC) sites during the period 2000–2009. We also used a modern-era retrospective analysis for research and applications (MERRA) dataset, the Normalized Difference Vegetation Index (NDVI) and Fractional Photosynthetically Active Radiation (FPAR) from the moderate resolution imaging spectroradiometer (MODIS) products; the leaf area index (LAI) from the global land surface satellite (GLASS) products; and the digital elevation model (DEM) from shuttle radar topography mission (SRTM30) dataset to generate LE at region scale during the period 2003–2006. The models were the moderate resolution imaging spectroradiometer LE (MOD16) algorithm, revised remote sensing based Penman–Monteith LE algorithm (RRS), the Priestley–Taylor LE algorithm of the Jet Propulsion Laboratory (PT-JPL), the modified satellite-based Priestley–Taylor LE algorithm (MS-PT), and the semi-empirical Penman LE algorithm (UMD). Direct comparison with ground measured LE showed the PT-JPL and MS-PT algorithms had relative high performance over semiarid ecosystems with the coefficient of determination (R2) ranging from 0.6 to 0.8 and root mean squared error (RMSE) of approximately 20 W/m 2 . Empirical parameters in the structure algorithms of MOD16 and RRS, and calibrated coefficients of the UMD algorithm may be the cause of the reduced performance of these LE algorithms with R2 ranging from 0.5 to 0.7 and RMSE ranging from 20 to 35 W/m 2 for MOD16, RRS and UMD. Sensitivity analysis showed that radiation and vegetation terms were the dominating variables affecting LE Fluxes in global semiarid ecosystem.

97 MATHEMATICS AND COMPUTING↗

Big Impacts and Transient Oceans on Titan

We have studied the thermal consequences of very big impacts on Titan [1]. Titan's thick atmosphere and volatile-rich surface cause it to respond to big impacts in a somewhat Earth-like manner. Here we construct a simple globally-averaged model that tracks the flow of energy through the environment in the weeks, years, and millenia after a big comet strikes Titan. The model Titan is endowed with 1.4 bars of N2 and 0.07 bars of CH4, methane lakes, a water ice crust, and enough methane underground to saturate the regolith to the surface. We assume that half of the impact energy is immediately available to the atmosphere and surface while the other half is buried at the site of the crater and is unavailable on time scales of interest. The atmosphere and surface are treated as isothermal. We make the simplifying assumptions that the crust is everywhere as methane saturated as it was at the Huygens landing site, that the concentration of methane in the regolith is the same as it is at the surface, and that the crust is made of water ice. Heat flow into and out of the crust is approximated by step-functions. If the impact is great enough, ice melts. The meltwater oceans cool to the atmosphere conductively through an ice lid while at the base melting their way into the interior, driven down in part through Rayleigh-Taylor instabilities between the dense water and the warm ice. Topography, CO2, and hydrocarbons other than methane are ignored. Methane and ethane clathrate hydrates are discussed quantitatively but not fully incorporated into the model.

methane↗