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A technique is described which can be used to evaluate Jacobian determinants which occur in classical mechanical and quasiclassical approximation descriptions of molecular scattering. The method may be valuable in the study of reactive scattering using the quasiclassical approximation.
Sampling techniques have been used previously to evaluate Jacobian determinants that occur in classical mechanical descriptions of molecular scattering. These determinants also occur in the quasiclassical approximation. A new technique is described which can be used to evaluate Jacobian determinants which occur in either description. This method is expected to be valuable in the study of reactive scattering using the quasiclassical approximation.
The results of computations of the Comptomization of low frequency radiation in weakly relativistic plasma are presented. The influence of photoabsorption by iron ions on a hard X-ray spectrum is considered.
A refined algorithm for generating emission frequencies from angle-dependent partial frequency redistribution functions R sub II and R sub III is described. The improved algorithm has as its basis a 'rejection' technique that, for absorption frequencies x less than 5, involves no approximations. The resulting procedure is found to be essential for effective studies of radiative transfer in optically thick or temperature varying media involving angle-dependent partial frequency redistributions.
The flow in the immediate vicinity of a rocket nozzle lip has been analyzed, and the results are presented. A rapid change in gas composition is observed in the flow around the lip depending principally on species molecular mass and local flow angle. The divergence of axial and radial temperatures indicating breakdown of translational equilibrium is observed in the results.
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A theory which gives statistical predictions for how often sonic booms propagating through the earth's turbulent boundary layer will encounter caustics, given the spectral properties of the atmospheric turbulence, is outlined. The theory is simple but approximately accounts for the variation of ray tube areas along ray paths. This theory predicts that the variation of ray tube areas is determined by the product of two similar area factors, psi (x) and phi (x), each satisfying a generic harmonic oscillator equation. If an area factor increases the peak acoustic pressure decreases, and if the factor decreases the peak acoustic pressure increases. Additionally, if an area factor decreases to zero and becomes negative, the ray has propagated through a caustic, which contributes a phase change of 90 degrees to the wave. Thus, it is clear that the number of times that a sonic boom wave passes through a caustic should be related to the distorted boom waveform received on the ground. Examples are given based on a characterization of atmospheric turbulence due to the structure function of Tatarski as modified by Crow.
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One of the main obstacles to the applications of Dempster-Shafer formalism is its computational complexity. If we combine m different pieces of knowledge, then in general case we have to perform up to 2(sup m) computational steps, which for large m is infeasible. For several important cases algorithms with smaller running time were proposed. We prove, however, that if we want to compute the belief bel(Q) in any given query Q, then exponential time is inevitable. It is still inevitable, if we want to compute bel(Q) with given precision epsilon. This restriction corresponds to the natural idea that since initial masses are known only approximately, there is no sense in trying to compute bel(Q) precisely. A further idea is that there is always some doubt in the whole knowledge, so there is always a probability p(sub o) that the expert's knowledge is wrong. In view of that it is sufficient to have an algorithm that gives a correct answer a probability greater than 1-p(sub o). If we use the original Dempster's combination rule, this possibility diminishes the running time, but still leaves the problem infeasible in the general case. We show that for the alternative combination rules proposed by Smets and Yager feasible methods exist. We also show how these methods can be parallelized, and what parallelization model fits this problem best.
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