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We describe a method for calculating directly the mean integrated intensity in an inhomogeneous Rayleigh scattering atmosphere using a combined variational and iterative technique. This method is particularly useful for computing dissociation rates in aeronomical problems. Simple semi-analytic expressions are derived.
Staged combustion, such as Rich-Burn/Quick-Mix/Lean-Burn (RQL), is a viable strategy to meet nitric oxide (NO) emission goals for both stationary and propulsion gas turbine engines. A critical element of the design is the quick mixer section where the potential for NO production is high. While numerical calculations of the quick mixer under reacting conditions have been conducted, the hostile environment and lack of appropriate diagnostics have, to date, precluded experimental probing of the reacting case. As an alternative to understanding the effect of geometry and flow variations on the production of NO in the quick mixer, the present paper presents (1) a series of non-reacting parametric studies, and (2) a computational method to extrapolate the results of the non-reacting experiments to reacting conditions. The results show that the rate of NO production is highest in the immediate vicinity of the injection plane. For a given momentum flux ratio between the jets and mainstream, the most effective mixing geometry is that which mixes effectively in both (1) the plane of injection, and (2) the wall regions downstream of the plan of injection. The tailoring of the mixing is key to minimize the NO formed. As a result, the best overall mixer with respect to the minimization of NO production may depend on the system specific characteristics of the particular application.
We proposed to investigate and develop better models for the effect of the hydrostatic and water vapor components of the neutral atmosphere on delay for VLBI and GPS by using a Numerical Weather Model to better simulate realistic atmosphere conditions. By using a raytrace calculation through the model atmosphere at the times of actual VLBI observations, the potential improvement in geodetic results can be evaluated. Also, by calculating the actual variation of delays with elevation and azimuth, the errors in current mapping function models can be assessed. The VLBI data to be initially analyzed are the fifteen days of the CONT02 sessions of 2002 October which included eight stations. There are three segments to the research. 1) The PSU/NCAR fifth generation mesoscale numerical weather model (MM5) will be used to provide the state of the atmosphere with highest horizontal resolution of 3 km. 2) A three-dimensional raytrace program will be developed to determine the delays through the model atmosphere at the times and in the directions of the VLBI observations for each of the sites. 3) The VLBI data will be analyzed using both standard models for the atmosphere mapping functions and the mapping functions derived from the NWM raytracing.
We analyze the time variation of microwave spectra and hard X-ray spectra of 1989 March 18, which are obtained from the Solar Array at the Owens Valley Radio Observatory (OVRO) and the Hard X-Ray Burst Spectrometer (HXRBS) on the Solar Maximum Mission (SMM), respectively. From this observation, it is noted that the hard X-ray spectra gradually soften over 50 - 200 keV on-and-after the maximum phase while the microwaves at 1 - 15 GHz show neither a change in spectral shape nor as rapid a decay as hard X-rays. This leads to decoupling of hard X-rays from the microwaves in the decay phase away from their good correlation seen in the initial rise phase. To interpret this observation, we adopt a view that microwave-emitting particles and hard X-ray particles are physically separated in an inhomogeneous magnetic loop, but linked via interactions with the Whistler waves generated during flares. From this viewpoint, it is argued that the observed decoupling of microwaves from hard X-rays may be due to the different ability of each source region to maintain high energy electrons in response to the Whistler waves passing through the entire loop. To demonstrate this possibility, we solve a Fokker-Planck equation that describes evolution of electrons interacting with the Whistler waves, taking into account the variation of Fokker-Planck coefficients with physical quantities of the background medium. The numerical Fokker-Planck solutions are then used to calculate microwave spectra and hard X-ray spectra for agreement with observations. Our model results are as follows: in a sronger field region, the energy loss by electron escape due to scattering by the waves is greatly enhanced resulting in steep particle distributions that reproduce the observed hard X-ray spectra. In a region with weaker fields and lower density, this loss term is reduced allowing high energy electrons to survive longer so that microwaves can be emitted there in excess of hard X-rays during the decay phase of the flare. Our results based on spectral fitting of a flare event are discussed in comparison with previous studies of microwaves and hard X-rays based on either temporal or spatial information.
Ab initio molecular dynamics (AIMD) is a valuable technique for studying molecules and materials at finite temperatures where the nuclei evolve on potential energy surfaces obtained from accurate electronic structure calculations. In this work, we present an approach to running AIMD simulations on noisy intermediate-scale quantum (NISQ)-era quantum computers. The electronic energies are calculated on a quantum computer using the variational quantum eigensolver (VQE) method. Algorithms for computation of analytical gradients entirely on a quantum computer require quantum fault-tolerant hardware, which is beyond NISQ-era. Therefore, we compute the energy gradients numerically using finite differences, the Hellmann-Feynman theorem, and a correlated sampling technique. This method only requires additional classical calculations of electron integrals for each degree of freedom without any additional computations on a quantum computer beyond the initial VQE run. As a proof of concept, AIMD simulations are demonstrated for the H-2 molecule on IBM quantum devices. In addition, we demonstrate the validity of the method for larger molecules using full configuration interaction wave functions. As quantum hardware and noise mitigation techniques continue to improve, the method can be utilized for studying larger molecular systems.
A numerical gasdynamic model, which includes the effects of mass loading of the shocked solar wind, was used to calculate the density and magnetic field variations in the magnetosheath of Venus. These calculations were carried out for conditions corresponding to a specific orbit of the Pioneer Venus Orbiter (PVO orbit 582). A comparison of the model predictions and the measured shock position, density and magnetic field values showed a reasonable agreement, indicating that a gasdynamic model that includes the effects of mass loading can be used to predict these parameters.
The results of a numerical simulation of the expansion of an H(+)-0(+) electron plasma into a vacuum are reported. Variations were introduced in the ionic density ratios, the scale lengths for the density gradient at the plasma-vacuum interface, and the initial electron-ion temperature ratio. Conditions of a gravitationally bound O(+) plasma were also considered. It was found that if H(+) is a major ion, the H(+) density profile in the expansion region is always concave, with a phase-space divided into three regions, i.e., an undisturbed plasma, a rarefaction region, and an expansion region in which ions are accelerated. When the H(+) is a minor ion, the O(+) ions accelerate the H(+) ions, the H(+) phase-space is divided into five regions, and the increased electron temperatures produce enhanced electrostatic potentials and H(+) drifts in the expansion region.
This study presents an example of how outputs of operational and readily-available mesoscale numerical models can be adapted to initialize dispersion calculations within the urban surface roughness layer. Three years of urban meteorological observations from central Washington, DC, are compared against forecast outputs of the North American Mesoscale (NAM) model. NAM wind speed predictions underestimate the observations in light winds and overestimate the measurements in high winds. Average wind directions are consistent. However, an adjustment of the predicted direction of the plume by –20° is needed. The uncertainty associated with this adjustment is large in light NAM wind speed with no evident variation by season. The values of the standard deviation of the wind direction, σθ derived from NAM model outputs underestimate the observations by a small amount (about –1.5 to –2.5°). The results presented here indicate that mesoscale numerical model outputs can provide information adequate for dispersion calculations. However, levels of uncertainty associated with implementation of the suggested procedures increase with decreasing wind speed, causing considerable uncertainty in the implementation of adjustments as low wind speed conditions are approached. Results and recommendations reported here should not be extended to other numerical models or other cities without further testing.
An analytical approach is presented that provides qualitative insight into both observations and numerical calculations of cosmic-ray electron modulation and embodies, as a natural feature of a specific model, two cosmic-ray components whose temporal variations are uncorrelated. In the light of this approach, it is shown that the origin and time variations of the steep spectrum of electrons observed below 20 MeV may be explained by a simple method in which the spectrum of interplanetary cosmic rays is decomposed at low energies into two independently varying components.
A large number of numerical models of gravitational microlensing by stars in the lensing galaxy have been calculated, and properties of the models are described. The expected light intensity variations are more rapid when optical depth to microlensing is large, but the time scale is a few years in the best cases, and much longer in a typical case. However, microlensing introduces considerable scatter, up to two or three orders of magnitude, to the intensity of macroimages expected at any given time, and this may considerably complicate the analysis of the observed lenses. It is shown that macroimage is surrounded with a faint 'halo' made of a large number of microimages from individual stars with average surface brightness falling off as R to the -4th. It is also shown that a high surface mass density of continuously distributed matter may affect very strongly properties of microlensing, making possible very large declines in observed intensity, up to two or three orders of magnitude.
Monte Carlo simulated lateral distribution functions for electrons of EPC developing in lead, at superhigh energies (.1-1 PeV) for depths t or = 60 c.u. delta t=1t. c.u. are presented. The higher moment characteristics, i.e., variation, asymmetry, excess, are presented along with analytical solutions for the same characteristics at fixed observation level calculated to theory approximations A and B by using numerical inversion of the Laplace transformation. The conclusion is made of a complex, usually non-Gaussian shape of the function of the particle number distribution within a circle of given radius at fixed depth.
A one-parameter family of explicit and implicit total variation diminishing (TVD) schemes is developed which permits incorporation of an expanded group of slope and flux limiters. The numerical technique is intended for use in calculations which include a time-differencing scheme and an optional Lax-Wendroff scheme. Methods of extending the TVD models to nonlinear scalar equations and systems of hyperbolic conservation equations are described. Sample results are presented from calculations of shocked flows around NACA 0012 and NACA 0018 airfoils.
Predictions using boundary-layer theory with a low-Reynolds number kinetic-energy/dissipation turbulence model are reported for the unsteady heat-flux distributions on the rotor blade surfaces. With an assumed sinusoidal variation for the unsteady surface pressure depicting the effects of convected wake segments, unsteady inviscid-freestream velocity and total enthalpy distributions are determined. Unsteady variations in freestream turbulence due to the wake passings are also considered. The unsteady boundary-layer equations, subject to these freestream conditions, are solved numerically. It was found that most of the unsteady variations in surface heat transfer are due to unsteady pressure changes and not variations in the freestream turbulence. Calculations are made for the Garrett TFE 731-2 HP turbine and the magnitudes of the heat-transfer variations are compared with the measurements of Dunn and Seymour.
A study is made of a predictor-corrector procedure for the accurate determination of the temperature and heat flux distributions in thick multilayered composite plates and shells. A linear through-the-thickness temperature distribution is used in the predictor phase. The functional dependence of temperature on the thickness coordinate is then calculated a posteriori and used in the corrector phase. Extensive numerical results are presented for linear steady-state heat conduction problems, showing the effects of variation in the geometric and lamination parameters on the accuracy of the thermal response predictions of the predictor-corrector approach. Both antisymmetrically laminated anisotropic plates and multilayered orthotropic cylinders are considered. The solutions are assumed to be periodic in the surface coordinates. For each problem the standard of comparison is taken to be the analytic three-dimensional solution based on treating each layer as a homogeneous anisotropic medium. The potential of the predictor-corrector approach for predicting the thermal response of multilayered plates and shells with complicated geometry is discussed.
A moment method for computing 3D radiative transport in axisymmetric thermochemical nonequilibrium flows is developed. The method uses the P-1 approximation to reduce the governing system of integro-differential equations to a coupled set of partial differential equations. The numerical solution of these equations for realistic variations of the radiation properties is discussed. Representative results from the method are shown and compared to tangent slab calculations. The agreement between the transport methods is found to be about 10 percent in the stagnation region, with the difference increasing along the flank of the vehicle.
The calculation of the phenomena within the boundary layer of bodies immersed in a flow underwent a decisive development on the basis of L. Prandtl's trains of thought, stated more than forth years ago, and by numerous later treatises again and again touching upon them. The requirements of the steadily improving aerodynamics of airplanes have greatly increased with the passing of time and recently research became particularly interested in such phenomena in the boundary layer as are caused by small external disturbances. Experimental results suggest that, for instance, slight fluctuations in the free stream velocities as they occur in wind tunnels or slight wavelike deviations of outer wing contours from the prescribed smooth course as they originate due to construction inaccuracies may exert strong effects on the extent of the laminar boundary layer on the body and thus on the drag. The development of turbulence in the last part of the laminar portion of the boundary layer is, therefore, the main problem, the solution of which explains the behavior of the transition point of the boundary layer. A number of reports in literature deal with this problem,for instance, those of Tollmien, Schlichting, Dryden, and Pretsch. The following discussion of the behavior of the laminar boundary layer for periodically oscillating pressure variation also purports to make a contribution to that subject.
The numerical calculation of local mass distributions in membrane systems by computational fluid dynamics (CFD) offers indispensable benefits. However, the concept to calculate such distributions in response to separate variations of operation conditions (OCs) makes it difficult to address overall, flow-physics-related questions, which require the consideration of the collective interaction of OCs. It is shown that such understanding-related relationships can be obtained by the analytical solution of the advection–diffusion equation considered. A Fourier series model (FSM) is presented, which provides exact solutions of an advection–diffusion equation for a wide range of OCs. On this basis, a new zeroth-order model is developed, which is very simple and as accurate as the complete FSM for all conditions of practical relevance. Advection-dominated blocked and diffusion-dominated unblocked flow regimes are identified (depending on a Péclet number which compares the flow geometry with a length scale imposed by the flow), which implies relevant requirements for the use of lab results for pilot- and full-scale applications. Analyses reveal the equivalence of variations of OCs, which offers a variety of options to accomplish desired flow regime changes.
The principle of local similarity, which has been used to model the two-dimensional boundary layers in the oceanic upper mantle, permits calculation of the temperature, velocity, and stress fields with essentially analytic techniques. Finite difference numerical methods are hard pressed to resolve the detail required by the large variation of viscosity between the lithosphere and the asthenosphere. In this paper the local similarity approximation has been justified by quantitatively evaluating the effect of nonsimilarity due to viscous heating, nonlinear temperature- and pressure-dependent rheology, buoyancy, adiabatic cooling, etc. Nonsimilar effects produce only small modifications of the locally similar boundary layers; important geophysical observables such as surface heat flux and ocean floor topography are given to better than 10 percent by the locally similar solution. A posteriori evaluations of the terms neglected in the boundary layer simplification of the complete equations have been conducted on the locally similar temperature and velocity profiles close to the spreading ridge. The boundary layer models are valid to depths of 100 km at 3 m.y. and 10 km at 0.3 m.y.