Random independent splitting model for the mass spectrum of protostars and interstellar clouds

Mathematical model for mass spectra of protostars and interstellar cloud

Covariance function of elevations on a cratered planetary surface. Part 2 - Crater rim and ejecta blanket contribution

Covariance function of elevations on cratered planetary surfac

Distribution of elevations on a cratered planetary surface

Distribution of elevations on a cratered planetary surfac

Statistical models of lunar rocks and regolith

The mathematical, statistical, and computational approaches used in the investigation of the interrelationship of lunar fragmental material, regolith, lunar rocks, and lunar craters are described. The first two phases of the work explored the sensitivity of the production model of fragmental material to mathematical assumptions, and then completed earlier studies on the survival of lunar surface rocks with respect to competing processes. The third phase combined earlier work into a detailed statistical analysis and probabilistic model of regolith formation by lithologically distinct layers, interpreted as modified crater ejecta blankets. The fourth phase of the work dealt with problems encountered in combining the results of the entire project into a comprehensive, multipurpose computer simulation model for the craters and regolith. Highlights of each phase of research are given

Semiclassical collision theory. Multidimensional integral method

Numerical results on the integral expression for the semiclassical S matrix are compared with exact quantum results for a multidimensional problem. The collision of a rigid rotor with an atom is treated. The integral method proves to be easy to apply. Within its range of maximum validity (no sign changes in the pre‐exponential factor of the semiclassical wavefunction) the agreement was typically within 20%. When sign changes occurred, the agreement was about a factor of 2 or better. Conditions affecting sign changes are described

The highly excited C-H stretching states of CHD_3, CHT_3, and CH_3D

Unlike many other molecules having local modes, the highly excited C-H stretching states of CHD_3 show well resolved experimental spectra and simple Fermi resonance behavior. In this paper the local mode features in this prototype molecule are examined using a curvilinear coordinate approach. Theory and experiment are used to identify the vibrational state coupling. Both kinetic and potential terms are employed in order to characterize the coupling of the C-H stretch to various other vibrational modes, notably those including D-C-H bending. Predictions are also made for CHT_3 and the role of dynamical coupling on the vibrational states of CH_3D explored. Implications of these findings for mode-specific and other couplings are discussed

Semiclassical collision theory. Multidimensional Bessel uniform approximation

A multidimensional Bessel uniform approximation for the semiclassical S matrix is derived for the case of four real stationary phase points. A formula is also developed for the particular case when four stationary phase points may be considered to be well separated in pairs. The latter equation is then used in the treatment of two real and two complex stationary phase points

Semiclassical collision theory. Application of multidimensional uniform approximations to the atom-rigid-rotor system

The multidimensional Bessel and Airy uniform approximations developed earlier in this series for the semiclassical S matrix are applied to the atom rigid−rotor system. The need is shown for (a) using a geoemetrical criterion for determining whether a stationary phase point (s.p.pt) is a maximum, minimum, or saddle point; (b) choosing a proper quadrilateral configuration of the s.p.pts. with the phases as nearly equal as possible; and (c) choosing a unit cell to favor near−separation of variables. (a) and (b) apply both to the Airy and to the Bessel uniform approximations, and (c) to the Bessel. The use of a contour plot both to understand and to facilitate the search in new cases is noted. The case of real and complex−valued stationary phase points is also considered, and the Bessel uniform−in−pairs approximation is applied. Comparison is made with exact quantum results. As in the one−dimensional case, the Bessel is an improvement over the Airy for ’’k = 0’’ transitions, while for other transitions they give similar results. Comparison in accuracy with the results of the integral method is also given. As a whole, the agreement can be considered to be reasonable. The improvement of the present over various more approximate results is shown