Scaling Solutions of Inelastic Boltzmann Equations with Over-Populated High Energy Tails

This paper deals with solutions of the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell models for large times and for large velocities, and the nonuniform convergence to these limits. We demonstrate how the velocity distribution approaches in the scaling limit to a similarity solution with a power law tail for general classes of initial conditions and derive a transcendental equation from which the exponents in the tails can be calculated. Moreover on the basis of the available analytic and numerical results for inelastic hard spheres and inelastic Maxwell models we formulate a conjecture on the approach of the velocity distribution function to a scaling form.     

A 1H and 13C NMR study of methoxyretinoids. Spectral assignment and determination of configuration

A number of modified retinals and retinoic esters carrying one or two methoxy groups or one methoxy and one methyl group on the polyene chain were investigated by ¹H and ¹³C NMR spectroscopy. Spectral assignments were made from homo- and selective ¹³C{¹H} hetero-decoupling experiments and from chemical shift comparisons. The configurations of the polyene double bonds were derived from vicinal H,H coupling constants, from ¹H and ¹³C chemical shifts and by measuring nuclear Overhauser enhancements. It is found that all double bonds with no additional substituents occur in the trans (E) and all methoxy-substituted double bonds in the cis (also E) configuration. Double bonds carrying methyl groups give rise to both cis (Z) and trans (E) isomers.     

Bulk properties from finite cluster calculations. VIII. Benchmark calculations of the efficiency of extrapolation methods for the HF and MP2 energies of polyacenes

The total energies per unit cell of both the undistorted and the Peierls-distorted polyacene polymers are computed from the respective HF/6-311G** and MP2/6-311G** finite-cluster data using 40 different extrapolation schemes. The benchmark calculations, which aim at assessing the efficiency of extrapolation methods, clearly show that the best procedure for obtaining rapidly converging bulk properties should involve computation of the energy differences, followed by rational extrapolation techniques such Wynn's p algorithm or its iteration, both with the interpolation points x_n = (n + 1)², and closely related extrapolation methods, or Wynn's ε algorithm and its close relative, Aitken's iterated Δ² algorithm. © John Wiley & Sons, Inc.     

Towards a Landau–Ginzburg-Type Theory for Granular Fluids

In this paper we show how, under certain restrictions, the hydrodynamic equations for the freely evolving granular fluid fit within the framework of the time dependent Landau–Ginzburg (LG) models for critical and unstable fluids. The granular fluid, which is usually modeled as a fluid of inelastic hard spheres (IHS), exhibits two instabilities: the spontaneous formation of vortices and of high density clusters. We suppress the clustering instability by imposing constraints on the system sizes, in order to illustrate how LG-equations can be derived for the order parameter, being the rate of deformation or shear rate tensor, which controls the formation of vortex patterns. From the shape of the energy functional we obtain the stationary patterns in the flow field. Quantitative predictions of this theory for the stationary states agree well with molecular dynamics simulations of a fluid of inelastic hard disks.     

Resonantly photo-pumped Fe16+ soft X-ray laser

A resonantly photo-pumped soft x-ray laser process is studied for neon-like iron ions with an automatic line match scheme. The special advantages of this scheme are shown. The temporal characteristics of lasing gains and their dependences on the pump strength and electron density are investigated. Unlike the electron-collisional excitation and some other photo-pumped excitation schemes, it is demonstrated that main photopumped gains come from 2p-4d-3p-3s transition channels. Using the experimental data of pump strengths from a non-LTE plasma produced in our experiment as input data, our model yields a peak gain of 5.6 cm^–1, 2.8 cm^–1 and 1.9 cm^–1 on the dominant lasing transitions at 38.74 nm, 25.47 nm and 20.46 nm.