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At least 253 records · Page 14

DIRECT NUMERICAL SIMULATION OF RADIATION PRESSURE-DRIVEN TURBULENCE AND WINDS IN STAR CLUSTERS AND GALACTIC DISKS

The pressure exerted by the radiation of young stars may be an important feedback mechanism that drives turbulence and winds in forming star clusters and the disks of starburst galaxies. However, there is great uncertainty in how efficiently radiation couples to matter in these high optical depth environments. In particular, it is unclear what levels of turbulence the radiation can produce, and whether the infrared radiation trapped by the dust opacity can give rise to heavily mass-loaded winds. In this paper, we report a series of two-dimensional flux-limited diffusion radiation-hydrodynamics calculations performed with the code ORION in which we drive strong radiation fluxes through columns of dusty matter confined by gravity in order to answer these questions. We consider both systems where the radiation flux is sub-Eddington throughout the gas column, and those where it is super-Eddington at the midplane but sub-Eddington in the atmosphere. In the latter, we find that the radiation-matter interaction gives rise to radiation-driven Rayleigh-Taylor instability, which drives supersonic turbulence at a level sufficient to fully explain the turbulence seen in Galactic protocluster gas clouds, and to make a non-trivial contribution to the turbulence observed in starburst galaxy disks. However, the instability also produces a channel structure in which the radiation-matter interaction is reduced compared to time-steady analytic models because the radiation field is not fully trapped. For astrophysical parameters relevant to forming star clusters and starburst galaxies, we find that this effect reduces the net momentum deposition rate in the dusty gas by a factor of {approx}2-6 compared to simple analytic estimates, and that in steady state the Eddington ratio reaches unity and there are no strong winds. We provide an approximation formula, appropriate for implementation in analytic models and non-radiative simulations, for the force exerted by the infrared radiation field in this regime.

79 ASTRONOMY AND ASTROPHYSICS↗

Methods and approximations for the computation of transmission profiles in the v4 band of methane in the atmosphere of Jupiter.

This note discusses the validity of certain band models and scaling approximations for computing transmissions in the v4 band of methane along inhomogeneous paths in the atmosphere of Jupiter. It is shown that Goody's random band model approximates the results of a rigorous numerical line-by-line calculation of the transmission profile of a Jovian model atmosphere.

Taylor, F. W.↗

Comparison of predicted and measured drag for a single-engine airplane

Renewed interest in natural laminar flow (NLF) has rekindled designers' concerns that manufacturing deviations, (loss of surface contours or other surface imperfections) may destroy the effectiveness of NLF for an operational airplane. This paper reports on experimental research that compares predicted and measured boundary layer transition, total drag, and two-dimensional drag coefficients for three different wing surface conditions on an airplane typical of general aviation manufacturing technology. The three flight test phases included: (1) assessment of an unpainted airframe, (2) flight tests of the same airplane after painstakingly filling and sanding the wings to design contours, and (3) similar measurements after this airplane was painted. In each flight phase, transition locations were monitored using either sublimating chemicals or pigmented oil. As expected, total drag changes were difficult to measure. Two-dimensional drag coefficients were estimated using the Eppler-Somers code and measured with a wake rake in a method very similar to Jones' pitot traverse method. The net change in two-dimensional drag was approximately 20 counts between the unpainted airplane and the 'hand-smoothed' airplane for typical cruise flight conditions.

Ward, D. T.↗

Flight Controllability Limits and Related Human Transfer Functions as Determined from Simulator and Flight Tests

A simulator study and flight tests were performed to determine the levels of static stability and damping necessary to enable a pilot to control the longitudinal and lateral-directional dynamics of a vehicle for short periods of time. Although a basic set of aerodynamic characteristics was used, the study was conducted so that the results would be applicable to a wide range of flight conditions and configurations. Novel piloting techniques were found which enabled the pilot to control the vehicle at conditions that were otherwise uncontrollable. The influence of several critical factors in altering the controllability limits was also investigated. Several human transfer functions were used which gave fairly good representations of the controllability limits determined experimentally for the short-period longitudinal, directional, and lateral modes. A transfer function with approximately the same gain and phase angle as the pilot at the controlling frequencies along the controllability limits was also derived.

Taylor, Lawrence W., Jr.↗

X-ray digital imaging petrography of lunar mare soils: modal analyses of minerals and glasses

It is essential that accurate modal (i.e., volume) percentages of the various mineral and glass phases in lunar soils be used for addressing and resolving the effects of space weathering upon reflectance spectra, as well as for their calibration such data are also required for evaluating the resource potential of lunar minerals for use at a lunar base. However, these data are largely lacking. Particle-counting information for lunar soils, originally obtained to study formational processes, does not provide these necessary data, including the percentages of minerals locked in multi-phase lithic fragments and fused-soil particles, such as agglutinates. We have developed a technique for modal analyses, sensu stricto, of lunar soils, using digital imaging of X-ray maps obtained with an energy-dispersive spectrometer mounted on an electron microprobe. A suite of nine soils (90 to 150 micrometers size fraction) from the Apollo 11, 12, 15, and 17 mare sites was used for this study. This is the first collection of such modal data on soils from all Apollo mare sites. The abundances of free-mineral fragments in the mare soils are greater for immature and submature soils than for mature soils, largely because of the formation of agglutinitic glass as maturity progresses. In considerations of resource utilization at a lunar base, the best lunar soils to use for mineral beneficiation (i.e., most free-mineral fragments) have maturities near the immature/submature boundary (Is/FeO approximately or = 30), not the mature soils with their complications due to extensive agglutination. The particle data obtained from the nine mare soils confirm the generalizations for lunar soils predicted by L.A. Taylor and D.S. McKay (1992, Lunar Planet Sci. Conf. 23rd, pp. 1411-1412 [Abstract]).

NASA Discipline Exobiology↗

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining the “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. As a result, in the limit of small shell thickness, exact thin-shell perturbationequations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation

We report the Boltzmann equation with the Bhatnagar-Gross-Krook collision model (Boltzmann-BGK equation) has been employed to describe multiscale flows, i.e., from the hydrodynamic limit to free molecular flow. In this study we employ physics-informed neural networks (PINNs) to solve forward and inverse problems via the Boltzmann-BGK formulation (PINN-BGK), enabling PINNs to model flows in both the continuum and rarefied regimes. In particular, the PINN-BGK is composed of three sub-networks, i.e., the first for approximating the equilibrium distribution function, the second for approximating the non-equilibrium distribution function, and the third one for encoding the Boltzmann-BGK equation as well as the corresponding boundary/initial conditions. By minimizing the residuals of the governing equations and the mismatch between the predicted and provided boundary/initial conditions, we can approximate the Boltzmann-BGK equation for both continuous and rarefied flows. For forward problems, the PINN-BGK is utilized to solve various benchmark flows given boundary/initial conditions, e.g. Kovasznay flow, Taylor-Green flow, cavity flow, and micro Couette flow for Knudsen number up to 5. For inverse problems, we focus on rarefied flows in which accurate boundary conditions are difficult to obtain. We employ the PINN-BGK to infer the flow field in the entire computational domain given a limited number of interior scattered measurements on the velocity without using the (unknown) boundary conditions. Results for the two-dimensional micro Couette and micro cavity flows with Knudsen numbers ranging from 0.1 to 10 indicate that the PINN-BGK can infer the velocity field in the entire domain with good accuracy. Finally, we also present some results on using transfer learning to accelerate the training process. Specifically, we can obtain a three-fold speedup comparted to the standard training process (e.g., Adam plus L-BFG-B) for the two-dimensional flow problems considered in our work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data

In this work, we present a machine learning approach to calculating electronic specific heat capacities for a variety of benchmark molecular systems. Our models are based on data from density matrix quantum Monte Carlo, which is a stochastic method that can calculate the electronic energy at finite temperature. As these energies typically have noise, numerical derivatives of the energy can be challenging to find reliably. In order to circumvent this problem, we use Gaussian process regression to model the energy and use analytical derivatives to produce the specific heat capacity. From there, we also calculate the entropy by numerical integration. We compare our results to cubic splines and finite differences in a variety of molecules in which Hamiltonians can be diagonalized exactly with full configuration interaction. We finally apply this method to look at larger molecules where exact diagonalization is not possible and make comparisons with more approximate ways to calculate the specific heat capacity and entropy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Augmenting subspace optimization methods with linear bandits

In this work, we consider the framework of methods for unconstrained minimization that are, in each iteration, restricted to a model that is only a valid approximation to the objective function on some affine subspace containing an incumbent point. These methods are of practical interest in computational settings where derivative information is either expensive or impossible to obtain. Recent attention has been paid in the literature to employing randomized matrix sketching for generating the affine subspaces within this framework. We consider a relatively straightforward, deterministic augmentation of such a generic subspace optimization method. In particular, we consider a sequential optimization framework where actions consist of one-dimensional linear subspaces and rewards consist of (approximations to) the magnitudes of directional derivatives computed in the direction of the action subspace. Reward maximization in this context is consistent with maximizing lower bounds on descent guaranteed by first-order Taylor models. This sequential optimization problem can be analysed through the lens of dynamic regret. We modify an existing linear upper confidence bound (UCB) bandit method and prove sublinear dynamic regret in the subspace optimization setting. We demonstrate the efficacy of employing this linear UCB method in a setting where forward-mode algorithmic differentiation can provide directional derivatives in arbitrary directions and in a derivative-free setting. For the derivative-free setting, we propose SS-POUNDers, an extension of the derivative-free optimization method POUNDers that employs the linear UCB mechanism to identify promising subspaces. Our numerical experiments suggest a preference, in either computational setting, for employing a linear UCB mechanism within a subspace optimization method.

97 MATHEMATICS AND COMPUTING↗

On incorporating damping and gravity effects in models of structural dynamics of the SCOLE configuration

The damping for structural dynamic models of flexible spacecraft is usually ignored and then added after modal frequencies and mode shapes are calculated. It is common practice to assume the same damping ratio for all modes, although it is known that damping due to bending and that due to torsion are sometimes ignored. Two methods of including damping in the modeling process from its onset are examined. First, the partial derivative equations of motion are analyzed for a pinned-pinned beam with damping. The end conditions are altered to handle bodies with mass and inertia for the Spacecraft Control Laboratory Experiment (SCOLE) configuration. Second, a massless beam approximation is used for the modes with low frequencies, and a clamped-clamped system is used to approximate the modes for arbitrarily high frequency. The model is then modified to include gravity effects and is compared with experimental results.

Taylor, Larry↗

Derivation of generalized transition/boundary conditions for planar multiple-layer structures

Infinite-order generalized impedance boundary conditions (GIBCs) and generalized sheet transition conditions (GSTCs) for planar multilayer configurations are developed via the Taylor series expansion method. The conditions are derived in a matrix product form where each matrix corresponds to a specific layer. An overall composite boundary/transition condition is obtained by making finite-order approximations to the elements of each matrix for the cases of 'low-contrast' and 'high-contrast' material layers. The accuracy of the truncated boundary conditions is examined by comparing their implied reflection and transmission coefficients with the corresponding exact coefficients. Design curves are also given which relate the maximum order of the conditions required to simulate a coating or layer of specific thickness and contrast. Expressions are then derived for the reflection and transmission coefficients of the GIBC/GSTC sheets, and these are compared to exact coefficients to demonstrate the validity of the derived GIBCs/GSTCs.

Ricoy, M. A.↗

Probing Venus's cloud structure with Galileo NIMS

The spectral image cubes obtained by the Near-Infrared Mapping Spectrometer (NIMS) on Galileo as it flew by Venus have been analyzed to constrain the vertical structure of the clouds, the nature of the aerosol particles, and the location and particle properties of the opacity variations responsible for high-contrast features observed in the near-infrared windows at 1.7 and 2.3 micrometers. A radiative transfer program was used to simulate mid-latitude curves of limb darkening at 3.7 micrometers. Best-fit models to these curves demonstrate that the upper clouds are dominated by mode 2 particles (r-bar = 1.0 micrometers), with a contribution of approximately 15% of opacity from mode 1 particles (r-bar = 0.3 micrometers). The low-latitude upper cloud is well represented by a dual scale-height model, with a particle scale height of approximately 1 km from an altitude of 61-63 km, and a scale height of approximately 6 km above this, up to the level where tau = 1 at approximately 71 km. This model also successfully simulates limb-darkening curves at 11.5 micrometers from the Pioneer Venus Orbiter Infrared Radiometer. Successful simulations of correlation plots of 1.7 vs 2.3 micrometers intensities reveal that mode 3 particles (r-bar = 3.65 micrometers) represent the dominant source of opacity in the lower and middle clouds, and that variation in total cloud opacity reflects chiefly the addition and removal of mode 3 particles near the cloud base. We find that the full spectrum of brightnesses at 1.7 and 2.3 micrometers implies that the total cloud optical depth varies from approximately 25 to approximately 40.

Grinspoon, D. H.↗

Paleo-Pole Positions from Martian Magnetic Anomaly Data

Magnetic component anomaly maps were made from five mapping cycles of the Mars Global Surveyor s magnetometer data. Our goal was to find and isolate positive and negative anomaly pairs which would indicate magnetization of a single source body. From these anomalies we could compute the direction of the magnetizing vector and subsequently the location of the magnetic pole existing at the time of magnetization. We found nine suitable anomaly pairs and from these we computed four North and 3 South poles with two at approximately 60 degrees north latitude. These results suggest that during the existence of the Martian main magnetic field it experienced several reversals.

Taylor, Patrick T.↗

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

An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 3-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first- and second-order statistical moment procedures are 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, these 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.↗

RELAXATION PROCESSES WITHIN FLUX ROPES IN SOLAR WIND

Flux ropes are localized structures in space plasma whose tube-like organized magnetic configuration can be well approximated by a force-free field model. Both numerical simulations and simple models suggest that the ideal magnetohydrodynamics (MHD) can relax toward a minimum energy state, where magnetic helicity is conserved, characterized by force-free magnetic fields (Taylor relaxation). In this paper, we evaluate MHD rugged invariants within more than 100 flux ropes identified in the solar wind at 1 AU, showing that the magnetic and cross-helicity content carried out by these structures tend to be “attracted” toward a particular subphase in the parameter plane. The final configuration of the MHD rugged invariants in the parameter plane suggests indeed that flux ropes represent well-organized structures coming from the dynamical evolution of MHD turbulent cascade. These observational results, along with a simple model based on a truncated set of nonlinear ordinary differential equations for both the velocity and magnetic field Fourier coefficients, thus, support a scenario in which the flux ropes naturally come out from the ideal MHD decay to large-scale magnetic field in space plasmas, probably governed by relaxation processes similar to those observed in laboratory plasmas.

79 ASTRONOMY AND ASTROPHYSICS↗

Polynominal Interpolation Methods for Viscous Flow Calculations

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and by Hermitian (Taylor series) finite-difference discretization. The similarities and special features of these different developments are discussed. The governing systems apply for both uniform and variable meshes. Hybrid schemes resulting from two different polynomial approximations for the first and second derivatives lead to a nonuniform mesh extension of the so-called compact or Pad? difference technique (Hermite 4). A variety of fourth-order methods are described and the Hermitian approach is extended to sixth-order (Hermite 6). The appropriate spline boundary conditions are derived for all procedures. For central finite differences, this leads to a two-point, second-order accurate generalization of the commonly used three-point end-difference formula. Solutions with several spline and Hermite procedures are presented for the boundary layer equations, with and without mass transfer, and for the incompressible viscous flow in a driven cavity. Divergence and nondivergence equations are considered for the cavity. Among the fourth-order techniques, it is shown that spline 4 has the smallest truncation error. The spline 4 procedure generally requires one-quarter the number of mesh points in a given coordinate direction as a central finite-difference calculation of equal accuracy. The Hermite 6 procedure leads to remarkably accurate boundary layer solutions.

Rubin, S. G.↗

Solution of the linear shallow water equations by the fourth-order leapfrog scheme

Numerical schemes of the first and second order of approximation introduce numerical distortion when the wave propagation over a long distance is investigated. To alleviate this problem, the fourth-order leapfrog scheme is constructed. The standard leapfrog method is based on the truncated Taylor series expansion which depicts an error proportional to the second-order terms. In the proposed method the numerical solution is corrected for these terms. The space and time corrections work well in diminishing numerical dispersion and dissipation.

Kowalik, Z.↗

A high-order Shifted Interface Method for Lagrangian shock hydrodynamics

Here, we present a new method for two-material Lagrangian hydrodynamics, which combines the Shifted Interface Method (SIM) with a high-order Finite Element Method. Our approach relies on an exact (or sharp) material interface representation, that is, it uses the precise location of the material interface. The interface is represented by the zero level-set of a continuous high-order finite element function that moves with the material velocity. This strategy allows to evolve curved material interfaces inside curved elements. By reformulating the original interface problem over a surrogate (approximate) interface, located in proximity of the true interface, the SIM avoids cut cells and the associated problematic issues regarding implementation, numerical stability, and matrix conditioning. Accuracy is maintained by modifying the original interface conditions using Taylor expansions. We demonstrate the performance of the proposed algorithms on established numerical benchmarks in one, two and three dimensions.

97 MATHEMATICS AND COMPUTING↗