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At least 235 records · Page 13

Three-layer interactive method for computing supersonic laminar separated flows

An interactive model for numerical computation of complicated two-dimensional flowfields including regions of reversed flow is proposed. The present approach is one of dividing the flowfield into three regions, in each of which a simplified mathematical model is applied: (1) outer, supersonic flow for which the full potential equation (hyperbolic) is used; (2) viscous, laminar layer in which the compressible boundary-layer model (parabolic) is used; and (3) recirculating flow modeled by the incompressible Navier-Stokes equations (elliptic). For matching of the numerical solutions in the three layers, two interaction models are developed: one for pressure interaction, the other for interaction between the shear layer and the recirculating flow. The uniform solution for the whole flowfield is then obtained by iteration of the local solutions under the constraints imposed by matching. The three-layer interactive model is used for solution of the flowfield past an asymmetric cavity. The method is shown to be capable of dealing with backflow without encountering problems at separation, characteristic to the boundary-layer approach.

Brandeis, J.↗

An Experimental and Theoretical Study of Radiative Extinction of Diffusion Flames

In a recent paper on 'Observations of candle flames under various atmospheres in microgravity' by Ross et al., it was found that for the same atmosphere, the burning rate per unit wick surface area and the flame temperature were considerably reduced in microgravity as compared with normal gravity. Also, the flame (spherical in microgravity) was much thicker and further removed from the wick. It thus appears that the flame becomes 'weaker' in microgravity due to the absence of buoyancy generated flow which serves to transport the oxidizer to the combustion zone and remove the hot combustion products from it. The buoyant flow, which may be characterized by the strain rate, assists the diffusion process to execute these essential functions for the survival of the flame. Thus, the diffusion flame is 'weak' at very low strain rates and as the strain rate increases the flame is initially 'strengthened' and eventually it may be 'blown out'. The computed flammability boundaries of T'ien show that such a reversal in material flammability occurs at strain rates around 5 sec. At very low or zero strain rates, flame radiation is expected to considerably affect this 'weak' diffusion flame because: (1) the concentration of combustion products which participate in gas radiation is high in the flame zone; and (2) low strain rates provide sufficient residence time for substantial amounts of soot to form which is usually responsible for a major portion of the radiative heat loss. We anticipate that flame radiation will eventually extinguish this flame. Thus, the objective of this project is to perform an experimental and theoretical investigation of radiation-induced extinction of diffusion flames under microgravity conditions. This is important for spacecraft fire safety.

Atreya, Arvind↗

Reinforcement Learning in a Nonstationary Environment: The El Farol Problem

This paper examines the performance of simple learning rules in a complex adaptive system based on a coordination problem modeled on the El Farol problem. The key features of the El Farol problem are that it typically involves a medium number of agents and that agents' pay-off functions have a discontinuous response to increased congestion. First we consider a single adaptive agent facing a stationary environment. We demonstrate that the simple learning rules proposed by Roth and Er'ev can be extremely sensitive to small changes in the initial conditions and that events early in a simulation can affect the performance of the rule over a relatively long time horizon. In contrast, a reinforcement learning rule based on standard practice in the computer science literature converges rapidly and robustly. The situation is reversed when multiple adaptive agents interact: the RE algorithms often converge rapidly to a stable average aggregate attendance despite the slow and erratic behavior of individual learners, while the CS based learners frequently over-attend in the early and intermediate terms. The symmetric mixed strategy equilibria is unstable: all three learning rules ultimately tend towards pure strategies or stabilize in the medium term at non-equilibrium probabilities of attendance. The brittleness of the algorithms in different contexts emphasize the importance of thorough and thoughtful examination of simulation-based results.

Bell, Ann Maria↗

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

An efficient incremental iterative approach for differentiating advanced flow codes is successfully demonstrated on a two-dimensional inviscid model problem. The method employs the reverse-mode capability of the automatic differentiation software tool ADIFOR 3.0 and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straightforward, black-box reverse-mode applicaiton of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-rder aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoinct) procedures; then, a very efficient noniterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hesian matrices) of lift, wave drag, and pitching-moment coefficients are calculated with respect to geometric shape, angle of attack, and freestream Mach number.

Taylor, Arthur C., III↗

Orbital simulations of satellite escape/capture and the origin of satellites such as Triton

We investigate satellite escape/capture in the context of the restricted, circular three body problem as applied to the Sun, Neptune, and Triton. We have computed a large number of coplanar prograde and retrograde orbital simulations over a range of initial distances and velocities. The satellite starts at superior conjunction within approximately 2 Hill radii of Neptune and has a velocity orthogonal to the Sun-planet line. Orbits with these initial conditions can be reflected with respect to time, so an escape is simply the reverse of a capture. We numerically integrate the equations of motion to compute the satellite's position until it escapes, collides with Neptune, or after 100 planetary years fails to escape, when computations cease. The initial distance x and velocity v in the restricted problem uniquely define the Jacobi constant C, a conserved energy-like quantity. Plots of the simulation outcomes in the prograde and retrograde C, x phase spaces reveal distinct zones in which temporary satellites approach the planet closely enough that permanent capture can be effected by gas drag with a protoplanetary nebula or by collision with a pre-existing satellite. Single and double close-flybys constitute the most common possible capture orbits. Long term multiple flyby orbits occur near the stability limits between bound and unbound orbits, and are more common among retrograde captures.

Benner, Lance A. M.↗

Periodicity of the earth's magnetic reversals

Results are presented from an attempt to perform a relatively comprehensive analysis of the evidence for a periodicity, with harmonics, of the observed regular reversals of the earth's magnetic field. The database considered covers 296 reversals over the past 165 Myr. Histograms with bins 1 Myr apart reveal only 30 Myr reversal patterns. The reversal dates are fitted to a linear periodic function and a spectrum is computed for the residuals at the adopted dates. The possible presence of multiple periodicities is evaluated and over various time intervals. The analysis shows that a recently observed 15 Myr periodicity is probably a harmonic of the 29.5-30.5 Myr period. The calculations do not confirm an inherent magnetic reversal property of the earth. The reversals may arise from tectonic events or from impacts from extraterrestrial objects.

Stothers, R. B.↗

POSTER: Automatic Differentiation of Parallel Loops with Formal Methods

The accompanying poster to this short paper presents a combination of reverse mode AD and formal methods to enable efficient differentiation of (or backpropagation through) shared-memory parallel code. Compared to the state of the art, our approach can more often avoid the need for atomic updates or private data copies during the parallel derivative computation, even in the presence of unstructured or data-dependent data access patterns. This is achieved by gathering information about the memory access patterns from the input program, which is assumed to be correctly parallelized. This information is then used to build a model of assertions in a theorem prover, which can be used to check the safety of shared memory accesses during the parallel derivative computation

Automatic Differentiation↗

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

An efficient incremental-iterative approach for differentiating advanced flow codes is successfully demonstrated on a 2D inviscid model problem. The method employs the reverse-mode capability of the automatic- differentiation software tool ADIFOR 3.0, and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straight-forward, black-box reverse- mode application of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-order aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoint) procedures; then, a very efficient non-iterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hessian matrices) of lift, wave-drag, and pitching-moment coefficients are calculated with respect to geometric- shape, angle-of-attack, and freestream Mach number

Taylor, Arthur C., III↗

Direct comparison between satellite electric field measurements and the visual aurora

Electric field data from two passes of the Injun 5 satellite, one corresponding to magnetically quiet conditions and one corresponding to substorm conditions, are compared with simultaneous all-sky-camera data from College, Alaska. In each case, a significant deviation of the electric field from the expected V x B field (where V is the satellite velocity) was evident and a distinct electric field reversal could be identified. In the region of substantial electric field equatorward of the electric field reversal a diffuse auroral arc was observed during the magnetically quiet pass and auroral patches were observed during the substorm pass. The motion of the auroral patches was consistent with the general direction and magnitude of the E x B drift computed from the satellite electric field measurements. In the substorm case the electric field reversal occurred very near a discrete auroral arc at the poleward side of the diffuse arcs and patches. Comparison of the quiet time and substorm cases suggests that the convection electric field penetrates deeper into the magnetosphere during a substorm.

Swift, D. W.↗

An experimental investigation of compressible three-dimensional boundary layer flow in annular diffusers

An experimental study is described in which detailed wall pressure measurements have been obtained for compressible three-dimensional unseparated boundary layer flow in annular diffusers with and without normal shock waves. Detailed mean flow-field data were also obtained for the diffuser flow without a shock wave. Two diffuser flows with shock waves were investigated. In one case, the normal shock existed over the complete annulus whereas in the second case, the shock existed over a part of the annulus. The data obtained can be used to validate computational codes for predicting such flow fields. The details of the flow field without the shock wave show flow reversal in the circumferential direction on both inner and outer surfaces. However, there is a lag in the flow reversal between the inner nad the outer surfaces. This is an interesting feature of this flow and should be a good test for the computational codes.

Om, Deepak↗

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Ibrahim, A. H.↗

Combining different 3-D global and regional seismic wave propagation solvers towards box tomography in the deep Earth

SUMMARY In previous publications, we presented a general framework, which we called ‘box tomography’, that allows the coupling of any two different numerical seismic wave propagation solvers, respectively outside and inside a target region, or ‘box’. The goal of such hybrid wavefield computations is to reduce the cost of computations in the context of full-waveform inversion for structure within the target region, when sources and/or receivers are located at large distances from the box. Previously, we had demonstrated this approach with sources and receivers outside the target region in a 2-D acoustic spherical earth model, and demonstrated and applied this methodology in the 3-D spherical elastic Earth in a continental scale inversion in which all stations were inside the target region. Here we extend the implementation of the approach to the case of a 3-D global elastic earth model in the case where both sources and stations are outside the box. We couple a global 3-D solver, SPECFEM3D_GLOBE, for the computation of the wavefield and Green’s functions in a reference 3-D model, with a regional 3-D solver, RegSEM, for the computation of the wavefield within the box, by means of time-reversal mirrors. We briefly review key theoretical aspects, showing in particular how only the displacement is needed to be stored at the boundary of the box. We provide details of the practical implementation, including the geometrical design of the mirrors, how we deal with different sizes of meshes in the two solvers, and how we address memory-saving through the use of B-spline compression of the recorded wavefield on the mirror. The proposed approach is numerically efficient but also versatile, since adapting it to other solvers is straightforward and does not require any changes in the solver codes themselves, as long as the displacement can be recovered at any point in time and space. We present benchmarks of the hybrid computations against direct computations of the wavefield between a source and an array of stations in a realistic geometry centred in the Yellowstone region, with and without a hypothetical plume within the ‘box’, and with a 1-D or a 3-D background model, down to a period of 20 s. The ultimate goal of this development is for applications in the context of imaging of remote target regions in the deep mantle, such as, for example, Ultra Low Velocity Zones.

Geochemistry & Geophysics↗

A conformational equilibrium in the nitrogenase MoFe protein with an α-V70I amino acid substitution illuminates the mechanism of H 2 formation

Study of α-V70I-substituted nitrogenase MoFe protein identified Fe6 of FeMo-cofactor (Fe 7 S 9 MoC-homocitrate) as a critical N 2 binding/reduction site. Freeze-trapping this enzyme during Ar turnover captured the key catalytic intermediate in high occupancy, denoted E 4 (4H), which has accumulated 4[e — /H + ] as two bridging hydrides, Fe2–H–Fe6 and Fe3–H–Fe7, and protons bound to two sulfurs. E 4 (4H) is poised to bind/reduce N 2 as driven by mechanistically-coupled H 2 reductive-elimination of the hydrides. This process must compete with ongoing hydride protonation (HP), which releases H 2 as the enzyme relaxes to state E 2 (2H), containing 2[e — /H + ] as a hydride and sulfur-bound proton; accumulation of E 4 (4H) in α-V70I is enhanced by HP suppression. EPR and 95 Mo ENDOR spectroscopies now show that resting-state α-V70I enzyme exists in two conformational states, both in solution and as crystallized, one with wild type (WT)-like FeMo-co and one with perturbed FeMo-co. These reflect two conformations of the Ile residue, as visualized in a reanalysis of the X-ray diffraction data of α-V70I and confirmed by computations. EPR measurements show delivery of 2[e — /H + ] to the E 0 state of the WT MoFe protein and to both α-V70I conformations generating E 2 (2H) that contains the Fe3–H–Fe7 bridging hydride; accumulation of another 2[e — /H + ] generates E 4 (4H) with Fe2–H–Fe6 as the second hydride. E 4 (4H) in WT enzyme and a minority α-V70I E 4 (4H) conformation as visualized by QM/MM computations relax to resting-state through two HP steps that reverse the formation process: HP of Fe2–H–Fe6 followed by slower HP of Fe3–H–Fe7, which leads to transient accumulation of E 2 (2H) containing Fe3–H–Fe7. In the dominant α-V70I E 4 (4H) conformation, HP of Fe2–H–Fe6 is passively suppressed by the positioning of the Ile sidechain; slow HP of Fe3–H–Fe7 occurs first and the resulting E 2 (2H) contains Fe2–H–Fe6. Importantly, it is this HP suppression in E 4 (4H) that enables α-V70I MoFe to accumulate E 4 (4H) in high occupancy. In addition, HP suppression in α-V70I E 4 (4H) kinetically unmasks hydride reductive-elimination without N 2 -binding, a process that is precluded in WT enzyme.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Phase diagram of the TIP4P/Ice water model by enhanced sampling simulations

In this work, we studied the phase diagram for the TIP4P/Ice water model using enhanced sampling molecular dynamics simulations. Our approach is based on the calculation of ice–liquid free energy differences from biased coexistence simulations that reversibly sample the melting and growth of layers of ice. We computed a total of 19 melting points for five different ice polymorphs, which are in excellent agreement with the melting lines obtained from the integration of the Clausius–Clapeyron equation. For proton-ordered and fully proton-disordered ice phases, the results are in very good agreement with previous calculations based on thermodynamic integration. For the partially proton-disordered ice III, we find a large increase in stability that is in line with previous observations using direct coexistence simulations for the TIP4P/2005 model. This issue highlights the robustness of the approach employed here for ice polymorphs with diverse degrees of proton disorder. Our approach is general and can be applied to the calculation of other complex phase diagrams.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Rupture Dynamics Simulations of Shallow Crustal Earthquakes on Reverse Slip Faults

The main goal of this study was to perform dynamic rupture simulations in order constrain the characterization of kinematic rupture models implemented in techniques for simulating strong ground motion for crustal earthquakes. First, we investigated the rupture process of the 2008 Iwate-Miyagi Nairiku earthquake by developing a dynamic rupture model on a reverse fault using a trial-and-error technique that produced a slip distribution and near-fault ground motion that matched the recorded ones. The simulations were performed in the frequency range 0-2 Hz, using a 3D staggered grid finite-difference method and a linear slip weakening friction law. Constrained by the observed slip distribution and consistent with dynamic rupture models, the derived kinematic rupture model of the Iwate-Miyagi Nairiku earthquake contains areas with relatively large slip rate, representing strong motion generation areas, set against lower amplitude heterogeneous background slip, and a relatively low slip rate in the weak zone of the top-most crust (upper 3km). Second, we performed rupture dynamics modeling to constrain shallow slip characterization in rupture models for strike-slip crustal earthquakes. The objective was to establish general rules about the characterization of slip rate function and slip at shallow depths and in the strong motion generation areas (SMGAs). The simulations of spontaneous rupture were performed in the frequency range 0-2.0Hz, using a 3D staggered-grid finite-difference method and a layer over half-space 1D crustal velocity model with a minimum shear-wave velocity of 2.8 km/s. In order to account for changes in material ductility and reduction of stress drop, observed in the shallow crust (upper 3-5 km), and the transition from ductile state to brittle state in the upper seismogenic zone, in our stress models we included a shallow weak zone (<4km). In this zone the stress drop was set to zero at the free surface and gradually increased with depth, while the slip weakening distance was set to 75 cm at the free surface and decreased to 50 cm at the base of the weak zone. As in the case of reverse faulting during the Iwate-Miyagi Nairiku earthquake, from these computations we found a systematic change in the shape of the slip-rate function, from Kostrov-type in the deeper part of the fault to a more symmetric cosine-type in the upper few kilometers, near the free-surface. Moreover, the average slip duration in the weak zone, with respect to slip duration in the deeper parts of the fault, increases by at most a factor of 1.5. We found a systematic and gradual change in the shape of the slip-rate function from Kostrov-type in the asperity areas (SMGAs), to more symmetric cosine-type in the upper few km near the free-surface, on the long period motion generation area (LMGA). The effective rise time in the LMGA, with respect to that in the SMGAs, increases by at most a factor of 2. Effective rise time is the time difference between the time at which the slip rate drops to a level that is equal to 25% of its peak and the onset time of the signal. In addition, the slip in the LMGA located above the SMGAs is almost the same as the one in the SMGAs, and about 1.5 times larger than the average slip.

58 GEOSCIENCES↗

Carbon monoxide oxidation rates computed for automobile thermal reactor conditions

Carbon monoxide oxidation rates in thermal reactors for exhaust manifolds are computed by integrating differential equations for system of twenty-nine reversible chemical reactions. Reactors are noncatalytic replacements for conventional exhaust manifolds and are a system for reducing carbon monoxide and hydrocarbons in automobile exhausts.

Brokaw, R. S.↗