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At least 325 records · Page 18

Mixing and Transition Control Studied

Considerable progress in understanding nonlinear phenomena in both unbounded and wallbounded shear flow transition has been made through the use of a combination of high- Reynolds-number asymptotic and numerical methods. The objective of this continuing work is to fully understand the nonlinear dynamics so that ultimately (1) an effective means of mixing and transition control can be developed and (2) the source terms in the aeroacoustic noise problem can be modeled more accurately. Two important aspects of the work are that (1) the disturbances evolve from strictly linear instability waves on weakly nonparallel mean flows so that the proper upstream conditions are applied in the nonlinear or wave-interaction streamwise region and (2) the asymptotic formulations lead to parabolic problems so that the question of proper out-flow boundary conditions--still a research issue for direct numerical simulations of convectively unstable shear flows--does not arise. Composite expansion techniques are used to obtain solutions that account for both mean-flow-evolution and nonlinear effects. A previously derived theory for the amplitude evolution of a two-dimensional instability wave in an incompressible mixing layer (which is in quantitative agreement with available experimental data for the first nonlinear saturation stage for a plane-jet shear layer, a circular-jet shear layer, and a mixing layer behind a splitter plate) have been extended to include a wave-interaction stage with a three-dimensional subharmonic. The ultimate wave interaction effects can either give rise to explosive growth or an equilibrium solution, both of which are intimately associated with the nonlinear self-interaction of the three dimensional component. The extended theory is being evaluated numerically. In contrast to the mixing-layer situation, earlier comparisons of theoretical predictions based on asymptotic methods and experiments in wall-bounded shear-flow transition have been somewhat lacking in one aspect or another. The current work strongly suggests that the main weakness is the underlying asymptotic representation of the linear "part" of the problem and not the explicit modeling of the nonlinear/wave-interaction effects. Consequently, the long-wave-length/high-Reynolds-number asymptotic limit for the Blasius boundary-layer stability problem was reexamined, and a new dispersion relationship for the instability waves that is uniformly valid for both the upper- and lower branch regions to the required order of approximation was obtained. A comparison with numerical results, obtained by solving the Orr-Sommerfeld stability problem, shows that the asymptotic formula provides surprisingly good results, even for values of the frequency parameter usually encountered in experimental investigations. This is particularly evident in the dynamically important upper-branch region, where much of the nonlinear interactions in transition experiments are believed to take place. The result is important in that it can be used to greatly improve the accuracy of weakly nonlinear critical-layer-based theories, and a consistent nonlinear theory is currently under evaluation.

Source record↗

Dynamical and Trace Gas Responses of the Quasi-Biennial Oscillation to Increased CO2

Long-term projections of the Quasi-Biennial Oscillation (QBO) remain uncertain. Using the high-top \Middle Atmosphere" (MA) version of the NASA Goddard Institute for Space Studies (GISS) ModelE (E2.2-AP), we show that increased CO2 reduces the QBO period and weakens its amplitude, consistent with results from recent multimodel studies. The amplitude response is asymmetric, with the easterly phase weakening more than the westerly phase. Results from both coupled atmosphere{ocean and climatologically fixed sea surface temperature simulations link the period response to changes in parameterized convective gravity wave fluxes, whereas the amplitude changes are more closely tied to changes in tropical upwelling. Comparisons of simulations with and without ozone-dynamical feedbacks reveal that ozone feedbacks increase the QBO amplitude and period in pre-industrial control simulations, and reduce the response of the amplitude to increased CO2. The response of stratospheric tracers to projected changes in the QBO is also investigated. Similarity between results using fully interactive (trace gas and aerosol) versus linearized ozone chemical mechanisms suggests that the QBO response to CO2 does not depend on additional chemical feedbacks beyond those associated with ozone, which implies that projected QBO changes may be credibly represented using simpli fied stratospheric ozone schemes.

GISS Model E2.2-AP↗

Model Checking A Self-Stabilizing Synchronization Protocol for Arbitrary Digraphs

This report presents the mechanical verification of a self-stabilizing distributed clock synchronization protocol for arbitrary digraphs in the absence of faults. This protocol does not rely on assumptions about the initial state of the system, other than the presence of at least one node, and no central clock or a centrally generated signal, pulse, or message is used. The system under study is an arbitrary, non-partitioned digraph ranging from fully connected to 1-connected networks of nodes while allowing for differences in the network elements. Nodes are anonymous, i.e., they do not have unique identities. There is no theoretical limit on the maximum number of participating nodes. The only constraint on the behavior of the node is that the interactions with other nodes are restricted to defined links and interfaces. This protocol deterministically converges within a time bound that is a linear function of the self-stabilization period. A bounded model of the protocol is verified using the Symbolic Model Verifier (SMV) for a subset of digraphs. Modeling challenges of the protocol and the system are addressed. The model checking effort is focused on verifying correctness of the bounded model of the protocol as well as confirmation of claims of determinism and linear convergence with respect to the self-stabilization period.

Malekpour, Mahyar R.↗

Exact relativistic expressions for polarization of incoherent Thomson scattering

We present a derivation of the degree of polarization for incoherent Thomson scattering (TS) using Mueller matrix formalism. An exact analytic solution is obtained for spectrum-integrated matrix elements. The solution is valid for the full range of incident polarizations, scattering angles, and electron thermal motion from non-relativistic to ultra-relativistic. It is based on a newly developed theoretical model, a finite transit time (FTT) correction to previous theoretical work on TS polarization. The Mueller matrix elements are substantially different from previous calculations without the FTT correction, even to the lowest linear order in T e =m e c 2 <<1. Mathematically, the derivation is a unique example of fully analytical integration of the 3D scattering operator over a relativistic Maxwellian distribution function; experimentally, the results have application to the use of the polarization properties of Thomson scattered light as a method of electron temperature measurement. The results can also be used as a reliable tool for benchmarking and verification of numerical codes for frequency resolved properties of TS polarization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Anomalous thermodynamic properties of quantum critical superconductors

Recent high-precision measurements employing different experimental techniques have unveiled an anomalous peak in the doping dependence of the London penetration depth which is accompanied by anomalies in the heat capacity in iron-pnictide superconductors at the optimal composition associated with the hidden antiferromagnetic quantum critical point. Here, we argue that finite temperature effects can be a cause of observed features. Specifically we show that quantum critical magnetic fluctuations under superconducting dome can give rise to a nodal-like temperature dependence of both specific heat and magnetic penetration depth in a fully gapped superconductor. In the presence of line nodes in the superconducting gap fluctuations can lead to the significant renormalization of the relative slope of T-linear penetration depth which is steepest at the quantum critical point. The results we obtain are general and can be applied beyond the model we use.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Equilibrium and Sudden Events in Chemical Evolution

We present new analytic solutions for one-zone (fully mixed) chemical evolution models that incorporate a realistic delay time distribution for Type Ia supernovae (SNe Ia) and can therefore track the separate evolution of αelements produced by core collapse supernovae (CCSNe) and iron peak elements synthesized in both CCSNe and SNe Ia. Our solutions allow constant, exponential, or linear–exponential (te{sup -t/τsfh}) star formation histories, or combinations thereof. In generic cases, α and iron abundances evolve to an equilibrium at which element production is balanced by metal consumption and gas dilution, instead of continuing to increase over time. The equilibrium absolute abundances depend principally on supernova yields and the outflow mass loading parameter η, while the equilibrium abundance ratio [α/Fe] depends mainly on yields and secondarily on star formation history. A stellar population can be metal-poor either because it has not yet evolved to equilibrium or because high outflow efficiency makes the equilibrium abundance itself low. Systems with ongoing gas accretion develop metallicity distribution functions (MDFs) that are sharply peaked, while “gas starved” systems with rapidly declining star formation, such as the conventional “closed box” model, have broadly peaked MDFs. A burst of star formation that consumes a significant fraction of a system’s available gas and retains its metals can temporarily boost [α/Fe] by 0.1–0.3 dex, a possible origin for rare, α-enhanced stars with intermediate age and/or high metallicity. Other sudden transitions in system properties can produce surprising behavior, including backward evolution of a stellar population from high to low metallicity.

79 ASTRONOMY AND ASTROPHYSICS↗

Thermal Expansion from Stochastic Nonlinear Acoustic Fields

The methods of stochastic mechanics are applied to nonlinear acoustic fields generated by random acoustic radiation sources associated with oscillating lattice sites in nonlinear lattices. The assumption of stochastically independent zero-point and temperature-dependent acoustic fields leads to expressions of the thermodynamic internal and Helmholtz free energies per unit mass in terms of modal energies per unit mass that account for the nonlinearity of the propagation modes. The thermodynamic state functions canonically transform to the familiar results of a system of quantized, simple harmonic oscillators in the linear field limit. The thermal expansion coefficient, derived from the Helmholtz free energy per unit mass, is obtained as a sum of the zero-point modal nonlinearity parameters, weighted by temperature-dependent, modal heat capacities. The relationship is fully anharmonic, in contrast to commonly used quasi-harmonic models, and predicts with excellent agreement the experimentally observed null thermal expansion of vitreous silica at the ‘cross-over’ temperature corresponding to the balance between long wavelength modes that contribute negative nonlinearity parameters to the modal sum and short wavelength modes that contribute positive nonlinearity parameters.

Cantrell, John H., Jr.↗

Boundary Layer Stability and Transition in a Chemically Reacting Martian Atmosphere Using LASTRAC

The Thermal Protection System (TPS) is a significant portion of the mass of reentry vehicles, planetary probes, and Martian entry vehicles. Reducing this mass has benefits in terms of decreased fuel requirements and increased payload; however, due to the high risk and uncertainty, the TPS or heat shields are designed conservatively by assuming fully turbulent flow. Laminar flow results in reduced heat flux, and improved transition prediction has the potential to reduce TPS mass and uncertainty in aerothermodynamic predictions. Limited previous research exists examining the problem of transition prediction for Martian atmospheric entry, with studies available on transition on the Mars Science Laboratory TPS. Although transition was demonstrated in wind-tunnel tests, uncertainty in the transition location resulted in a TPS designed for fully turbulent flow, and therefore greater mass than required for a partially laminar condition. In this work, we extend the boundary layer stability code LASTRAC, recently modified to include chemical and thermal nonequilibrium capabilities, to a model of the Martian atmosphere. LASTRAC provides Parabolized Stability Equations (PSE) as well as Linear Stability Theory (LST) to predict the stability of a boundary layer and transition with semi-empirical e(sup N) methods. Results included in this work compare disturbance growth characteristics between air and Martian atmosphere at similar non-dimensional freestream conditions on a simple flat plate geometry. Both chemical nonequilibrium and thermochemical nonequilibrium, as well as both PSE and LST, are used.

Kline, H. L.↗

Spontaneous magnetization of collisionless plasma

Here we study within a fully kinetic framework the generation of “seed” magnetic fields through the Weibel instability, driven in an initially unmagnetized plasma by a large-scale shear force. We develop an analytical model that describes the development of thermal pressure anisotropy via phase mixing, the ensuing exponential growth of magnetic fields in the linear Weibel stage, and the saturation of the Weibel instability when the seed magnetic fields become strong enough to instigate gyromotion of particles and thereby inhibit their free-streaming. The predicted scaling dependencies of the saturated fields on key parameters (e.g., ratio of system scale to electron skin depth and forcing amplitude) are confirmed by two-dimensional and three-dimensional particle-in-cell simulations of an electron–positron plasma. This work demonstrates the spontaneous magnetization of a collisionless plasma through large-scale motions as simple as a shear flow and therefore has important implications for magnetogenesis in dilute astrophysical systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

THERMAL DIAGNOSTICS WITH THE ATMOSPHERIC IMAGING ASSEMBLY ON BOARD THE SOLAR DYNAMICS OBSERVATORY: A VALIDATED METHOD FOR DIFFERENTIAL EMISSION MEASURE INVERSIONS

We present a new method for performing differential emission measure (DEM) inversions on narrow-band EUV images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory. The method yields positive definite DEM solutions by solving a linear program. This method has been validated against a diverse set of thermal models of varying complexity and realism. These include (1) idealized Gaussian DEM distributions, (2) 3D models of NOAA Active Region 11158 comprising quasi-steady loop atmospheres in a nonlinear force-free field, and (3) thermodynamic models from a fully compressible, 3D MHD simulation of active region (AR) corona formation following magnetic flux emergence. We then present results from the application of the method to AIA observations of Active Region 11158, comparing the region's thermal structure on two successive solar rotations. Additionally, we show how the DEM inversion method can be adapted to simultaneously invert AIA and Hinode X-ray Telescope data, and how supplementing AIA data with the latter improves the inversion result. The speed of the method allows for routine production of DEM maps, thus facilitating science studies that require tracking of the thermal structure of the solar corona in time and space.

79 ASTRONOMY AND ASTROPHYSICS↗

Bright and dark singlet excitons via linear and two-photon spectroscopy in monolayer transition metal dichalcogenides

We discuss the linear and two-photon spectroscopic selection rules for spin-singlet excitons in monolayer transition-metal dichalcogenides. Our microscopic formalism combines a fully k-dependent few-orbital band structure with a many-body Bethe-Salpeter equation treatment of the electron-hole interaction, using a model dielectric function. We show analytically and numerically that the single-particle, valley-dependent selection rules are preserved in the presence of excitonic effects. Furthermore, we definitively demonstrate that the bright (one-photon allowed) excitons have s-type azimuthal symmetry and that dark p-type excitons can be probed via two-photon spectroscopy. Thus, the screened Coulomb interaction in these materials substantially deviates from the 1/ε₀r form; this breaks the “accidental” angular momentum degeneracy in the exciton spectrum, such that the 2p exciton has a lower energy than the 2s exciton by at least 50 meV. We compare our calculated two-photon absorption spectra to recent experimental measurements.

36 MATERIALS SCIENCE↗

Analytic model of aurorally coupled magnetospheric and ionospheric electrostatic potentials

This paper describes modest but significant improvements on earlier studies of electrostatic potential structure in the auroral region using the adiabatic auroral arc model. This model has crucial nonlinearities (connected, for example. with aurorally produced ionization) which have hampered analysis; earlier work has either been linear, which I will show is a poor approximation or, if nonlinear, either numerical or too specialized to study parametric dependencies. With certain simplifying assumptions I find new analytic nonlinear solutions fully exhibiting the parametric dependence of potentials on magnetospheric (e.g.. cross-tail potential) and ionospheric (e.g., recombination rate) parameters. No purely phenomenological parameters are introduced. The results are in reasonable agreement with observed average auroral potential drops, inverted-V scale sizes, and dissipation rates. The dissipation rate is quite comparable to tail energization and transport rates and should have a major effect on tail and magnetospheric dynamics. This paper gives various relations between the cross-tail potential and auroral parameters (e.g., total parallel currents and potential drops) which can be studied with existing data sets.

Cornwall, J. M.↗

A Parallel, Finite-Volume Algorithm for Large-Eddy Simulation of Turbulent Flows

A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting, and second-order MacCormack time marching. Parallel implementation is done using the message-passing programming model. In this paper, the numerical algorithm is described. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. The effects of grid resolution, upwind numerical dissipation, and subgrid-scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe flux-difference splitting dissipation adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3-5 percent of the standard Roe flux-difference splitting dissipation is needed.

Bui, Trong T.↗

Boundary Layer Stability and Transition in a Chemically Reacting Martian Atmosphere using LASTRAC

The Thermal Protection System (TPS) is a significant portion of the mass of reentry vehicles, planetary probes, and Martian entry vehicles. Reducing this mass has benefits in terms of decreased fuel requirements and increased payload; however, due to the high risk and un-certainty, the TPS or heat shields are designed conservatively by assuming fully turbulent flow. Laminar flow results in reduced heat flux, and improved transition prediction has the potential to reduce TPS mass and uncertainty in aerothermodynamic predictions. Limited previous research exists examining the problem of transition prediction for Martian atmospheric entry, with studies available on transition on the Mars Science Laboratory TPS. Although transition was demonstrated in wind-tunnel tests, uncertainty in the transition location resulted in a TPS designed for fully turbulent flow, and therefore greater mass than required for a partially-laminar condition. In this work, we extend the boundary layer stability code LASTRAC, recently modified to include chemical and thermal nonequilibrium capabilities, to a model of the Martian atmosphere. LASTRAC provides Parabolized Stability Equations (PSE) as well as Linear Stability Theory (LST) to predict the stability of a boundary layer and transition with semi-empirical eN methods. Results included in this work compare disturbance growth characteristics between air and Martian atmosphere at similar nondimensional freestream conditions on a simple flat plate geometry. Both chemical nonequilibrium and thermochemical nonequilibrium, as well as both PSE and LST, are used.

Heather L Kline↗

Certification of a hybrid parameter model of the fully flexible Shuttle Remote Manipulator System

The development of high fidelity models of mechanical systems with flexible components is in flux. Many working models of these devices assume the elastic motion is small and can be superimposed on the overall rigid body motion. A drawback associated with this type of modeling technique is that it is required to regenerate the linear modal model of the device if the elastic motion is sufficiently far from the base rigid motion. An advantage to this type of modeling is that it uses NASTRAN modal data which is the NASA standard means of modal information exchange. A disadvantage to the linear modeling is that it fails to accurately represent large motion of the system, unless constant modal updates are performed. In this study, which is a continuation of a project started last year, the drawback of the currently used modal snapshot modeling technique is addressed in a rigorous fashion by novel and easily applied means.

Barhorst, Alan A.↗

Enantioselective Intramolecular Allylic Substitution via Synergistic Palladium/Chiral Phosphoric Acid Catalysis: Insight into Stereoinduction through Statistical Modeling

The mode of asymmetric induction in an enantioselective intramolecular allylic substitution reaction catalyzed by a combination of palladium and a chiral phosphoric acid was investigated by a combined experimental and statistical modeling approach. Experiments to probe nonlinear effects, the reactivity of deuterium-labeled substrates, and control experiments revealed that nucleophilic attack to the π-allylpalladium intermediate is the enantio-determining step, in which the chiral phosphate anion is involved in stereoinduction. Here, using multivariable linear regression analysis, we determined that multiple noncovalent interactions with the chiral environment of the phosphate anion are integral to enantiocontrol in the transition state. The synthetic protocol to form chiral pyrrolidines was further applied to the asymmetric construction of C-O bonds at fully substituted carbon centers in the synthesis of chiral 2,2-disubstituted benzomorpholines.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Scaling Behavior of Thermally Driven Fractures in Deep Low‐Permeability Formations: A Plane Strain Model With 1‐D Heat Conduction

Abstract Injection of cold fluids through/into deep formations may cause significant cooling, thermal stress, and possible thermal fracturing. In this study, the thermal fracturing of low‐permeability formations under one‐dimensional heat conduction was investigated using a plane strain model. Dimensionless governing equations, with dimensionless fracture length , aperture , spacing , time , and effective confining stress , were derived. Solution of single thermal fracture was derived analytically, while solution of multiple fractures with constant (or dynamic) spacing were obtained using the displacement discontinuity method (and stability analysis). For single fracture, increases nonlinearly with and then transitions to scaling law , indicating that late‐time fracture length increases linearly with the square root of cooling time. For constantly spaced fractures, deviates from the single‐fracture solution at a later for a larger , showing slower propagation under inter‐fracture stress interaction . For dynamically spaced fractures, fracture arrest induced by stress interaction was determined by the stability analysis; the fully transient solution provides evolution of dimensionless fracture length, spacing, aperture, and pattern; a similar scaling law, with , obtained shows the effect of both stress interaction and fracture arrest. The solution and scaling law provide fast predictions for all reservoir and cooling conditions using (single) model parameter . Application to a geothermal site with demonstrates that thermal fractures reach 0.67, 6.25, and 78.00 m in length, 0.49, 2.30, and 13.00 m in spacing, and 0.43, 2.09, and 12.19 mm in aperture at 1, 100, and 10,000 days.

Chen, Bin↗