Potential scattering in the generator Coordinate method

The generator coordinate formulation of the quantum-mechanical scattering problem transforms the solution of a problem in Hilbert space into an equivalent problem in Banach space. The structure of this problem is, however, that of an ill-posed problem. In order to shed some light onto the numerical intricacies, we investigate a number of potential scattering systems. One finds that, notwithstanding the numerical uncertainties of the weight function, excellent results for phase shifts (and scattering solutions) can be obtained.     

High-resolution laser excitation spectra of linear triatomic molecules: Analysis of the B2Σ+-X2Σ+ system of SrOH and SrOD

Single-mode cw dye laser excitation spectra of the (0, 0⁰, 0)-(0, 0⁰, 0), (1, 0⁰, 0)-(1, 0⁰, 0), (0, 1¹, 0)-(0, 1¹, 0) bands of the 611- to 607-nm system of SrOH and SrOD were observed and assigned. The spectrum is consistent with a ²Σ-²Σ system where the molecule is linear in both electronic states. The rotational analysis is obtained by measuring P-R separations in the excitation spectrum. A technique which greatly aided in the spectral assignment that utilizes a monochromator as a bandpass filter in obtaining excitation spectra is described. A new spin-rotation constant, γ⁽⁺⁾ - γ^(?), was found necessary to fit the l-type doubling of the (0, 1¹, 0) mode in B²Σ⁺ of SrOH. This new constant is assumed to arise from two ${}^2\text{Σ}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ vibronic states, split by Renner-Teller interaction, of the (0, 1¹, 0) mode of A²Π. From a perturbation treatment of this electronic interaction, ?ω₂ of the (0, 1¹, 0) mode of A²Π was found to be 14 cm^?1. The linear structure of SrOH and SrOD in both electronic states is consistent with the model, in the one-electron approximation, in that the transition involves the promotion of the unpaired 5s to the 5p orbital localized on the strontium.     

A model for the plane to plane variations in catalytic activity seen during nitric oxide decomposition on platinum

Previous work has shown that the reactivity of platinum for nitric oxide decomposition varies significantly with the geometry of the exposed surface of the platinum. Here, the available data are compared to the predictions of a model, which is based on conservation of orbital symmetry and a simplified picture of the band structure of the surface. The model predicts that the (100) face of platinum should be more active than either the (111) or the (110). The (410) should be more active still. These predictions agree with recent experiment. The model makes several other predictions which need to be tested experimentally. These results suggest that symmetry conservation methods, similar to the ones developed by Woodward and Hoffmann for organic reactions, could yield many valuable insights into the relative activity of various catalyst structures.     

Bifurcations in a model of magnetoconvection

Bifurcations from oscillatory solutions are studied in a truncated model of two-dimensional Boussinesq magnetoconvection. The fifth order system of nonlinear differential equations is integrated numerically and in certain parameter regimes there is a bifurcation from symmetrical to asymmetrical oscillations followed by a period-doubling cascade. After the accumulation point there is a semiperiodic cascade leading to chaotic behaviour. Then the semiperiodic cascade is repeated in reverse, followed by a period-halving cascade and a bifurcation back to symmetry. Finally, the branch of oscillatory solutions terminates with a symmetrical heteroclinic orbit that connects two saddle-foci. The interval with aperiodic solutions contains many pairs of narrow windows with asymmetrical or symmetrical periodic solutions, each with its own cascade. This pattern of behaviour is likely to occur when a periodic orbit approaches a symmetrical pair of saddle-foci with eigenvalues that satisfy Shil'nikov's inequality.     

Inverse problem of the determination of a nonlinear dependence of the electric current on the electric field intensity

Translated from Matematicheskie Zametki, Vol. 48, No. 3, pp. 81–90, September, 1990.     

On the Pesin set of expansive geodesic flows in manifolds with no conjugate points

In this paper, we show that the Pesin set of an expansive geodesic flow in compact manifold with no conjugate points and bounded asymptote coincides a.e with an open and dense set of the unit tangent bundle. We also show that the set of hyperbolic periodic orbits is dense in the unit tangent bundle.     

A Theorem on Multiplicators in Nonhomogeneous Hölder Spaces and Some of Its Applications

In Sec. 2, sufficient conditions of the boundedness of convolution operators with kernel m in a nonhomogeneous Hölder space are given in terms of the Fourier-image of m. After that, the results of Sec. 2 are used to prove the solvability in a Hölder space of the Cauchy problem for linear systems of the hydrodynamic type. Bibliography: 6 titles.     

On the Twisted Cubic of PG(3, q)

In this paper we classify the lines of PG(3, q) whose points belong to imaginary chords of the twisted cubic of PG(3, q). Relying on this classification result, we obtain a complete classification of semiclassical spreads of the generalized hexagon H(q).