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The calculations in this paper afford an approximate solution of the static stability. A derivation of the formulas for moment coefficient of a wing, moment coefficient of elevator, and the total moment of the combined wing and elevator and the moment coefficient with reference to the center of gravity are provided.
A simplified method for the calculation of radiative heat transfer in hypersonic reentry flows where local thermal nonequilibrium (LTNE) conditions exist is presented. This method has been incorporated into the computer code RADMC (RADiation/Modified Corrections), which utilizes an approximate 'two-state' model of the electronic levels of atoms and molecules in the determination of the populations of the excited states for both LTNE and local thermal equilibrium (LTE) conditions for each of the relevant chemical species. The population data are used to calculate a correction factor to the radiative cross sections in an eight-step nongray radiative heat-transfer model. Results have been obtained for various points along the proposed trajectory of the Aeroassist Flight Experiment and the Fire II trajectory, and compared with results obtained for the same flowfields from the NEQAIR radiative heat-transfer code.
Radiant energy transfer in absorbing and emitting media, noting approximate equations reduced to correct optically thin and thick limits for multidimensional problems
Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists.
Location and nature of singularity of Ising square lattice susceptibility, using Pade approximation based on Clapp spin-spin correlation function
The lattice expansion in ZnO, using in-situ X ray diffraction, has been investigated during flash sintering with varying current densities. While current flow through the specimen enhances the kinetics of sintering for ZnO, the temperature is not high enough to claim thermal runaway or localized melting. Unlike the case of yttria stabilized zirconia [1,2], experimental temperature approximations predict comparable specimen temperature to conventional sintering temperature of ZnO. Microstructural analysis supports the findings of the in-situ temperature approximations. In comparison with black body radiation, a gap between theoretical value and measured value was found due to flaws in the theoretical model. In addition, a new type of flash sintering was introduced, with current ramp, to avoid the power spike which has been the source of much debate about the transition from voltage to current control. In conclusion, the advantage of this method is in the controlled sintering kinetics thus avoiding the channeling found in dielectric materials [3].
From the solution of the time-dependent Schrödinger equation (TDSE), it has been shown that in a two-color laser pulse the relative phase that optimizes terahertz (THz) radiation also optimizes the asymmetry of the angular distribution of photoelectrons. Here, in this work, we show that a second-order strong-field approximation can accurately calculate the asymmetry of photoelectrons and thus can locate the phase delay that optimizes THz generation, doing so four orders of magnitude faster than TDSE calculations. We further trace that this is possible because THz emission originates from a free-free radiative transition between the rescattered electron and the target ion, similar to other electron-ion collisions in the laser field, e.g., high-harmonic generation and nonsequential double ionization. Our results pave the way to locate the optimal phase delay for any typical laser pulses for maximal THz generation in the laboratory.
A new algorithm for solving the duals of separable convex optimization problems is presented. The algorithm is based on an active set strategy in conjunction with a variable metric method. This first order algorithm is more reliable than Newton's method used in DUAL-2 because it does not break down when the Hessian matrix becomes singular or nearly singular. A perturbation technique is introduced in order to remove the nondifferentiability of the dual function which arises when linear constraints are present in the approximate problem.
A user's manual is presented for a computer program which calculates inviscid flow about lifting configurations in the free-stream Mach-number range from zero to low supersonic. Angles of attack of the order of the configuration thickness-length ratio and less can be calculated. An approximate formulation was used which accounts for shock waves, leading-edge separation and wind-tunnel wall effects.
The head-on collision of two nonrotating black holes, initially falling toward each other with speed of approach equal to escape velocity, is studied. The initial-value problem for the two-black-hole configuration is solved by giving the extrinsic curvature on a Euclidean space slice, with the equal masses of the two holes and their separation as free parameters. An approximating space-time is then constructed by stacking up a whole sequence of initial-value slices with decreasing separation between the black holes. The space-time singularities at the centers of the two black holes collide at some instant of time, and after that time the space-time so constructed is just the Schwarzschild solution with mass equal to the total mass of both black holes. The approximating space-time describes the coalescence of the event horizons, but contains no gravitational waves.
A theoretical model employing one-dimensional (depth) transport equations to describe vertical redistribution of ocean-floor and lake-floor sediment (particulates, volcanic ash, microtektites, or radioactive tracers) by episodic and nonepisodic events including bioturbation is developed analytically and demonstrated. The principles underlying the model are explained; the model equations are derived; the inverse problem of identifying the depth-dependent bioturbation coefficient is addressed; two approximation theorems are presented; and numerical results for two sample problems are presented graphically. It is suggested that compatification, porosity effects, and depth-dependent sedimentation be taken into account when formulating future models.
A major research and technology program in Probabilistic Structural Analysis Methods (PSAM) is currently being sponsored by the NASA Lewis Research Center with Southwest Research Institute as the prime contractor. This program is motivated by the need to accurately predict structural response in an environment where the loadings, the material properties, and even the structure may be considered random. The heart of PSAM is a software package which combines advanced structural analysis codes with a fast probability integration (FPI) algorithm for the efficient calculation of stochastic structural response. The basic idea of PAAM is simple: make an approximate calculation of system response, including calculation of the associated probabilities, with minimal computation time and cost, based on a simplified representation of the geometry, loads, and material. The deterministic solution resulting should give a reasonable and realistic description of performance-limiting system responses, although some error will be inevitable. If the simple model has correctly captured the basic mechanics of the system, however, including the proper functional dependence of stress, frequency, etc. on design parameters, then the response sensitivities calculated may be of significantly higher accuracy.
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Magnetohydrodynamic boundary layer and heat transfer of a conducting fluid past a cylindrical body
Problems in computing transition matrices of lunar trajectories