Inverse scattering from an open arc

A Newton method is presented for the approximate solution of the inverse problem to determine the shape of a sound-soft or perfectly conducting arc from a knowledge of the far-field pattern for the scattering of time-harmonic plane waves. Fréchet differentiability with respect to the boundary is shown for the far-field operator, which for a fixed incident wave maps the boundary arc onto the far-field pattern of the scattered wave. For the sake of completeness, the first part of the paper gives a short outline on the corresponding direct problem via an integral equation method including the numerical solution.     

A singular perturbation problem for linear operators with an application to electrostatic and magnetostatic boundary and transmission problems

The treatment of certain electro- and magnetostatic boundary and transmission problems by boundary integral equations leads to parameter-dependent integral equations of the second kind. The integral operators involved have the property that the dimension of their nullspaces changes between two nonzero values (depending on the geometry of the problem) as the parameter tends to zero. We investigate the continuous dependence of solutions to these equations on the parameter. To this end, we treat the problem of continuous dependence of solutions to parameter-dependent linear operator equations of the second kind in a Banach space in the framework of generalized inverses.     

Ein ableitungsfreies Restglied für die trigonometrische Interpolation periodischer analytischer Funktionen

Ohne Zusammenfassung     

Naphthyridine chemistry. VIII. The mass spectra of the 1,X-naphthyridines and some of their methyl derivatives

The mass spectra of the four parent 1,X-naphthyridines, the 2,3 and 4-monomethyl-1,5-,1,6-. and 1,8- naphthyridincs, seven dimethyl-1,8-naphthyridines, and one trimethyl-1,8-naphthyridine are reported. Evidence for an azatropylium ion intermediate in the fragmentation of the methyl compounds is presented. The fragmentation modes of the naphthyridines are similar to those for the quinolines in addition to several new processes     

A second degree Newton method for an inverse obstacle scattering problem

A regularized second degree Newton method is proposed and implemented for the inverse problem for scattering of time-harmonic acoustic waves from a sound-soft obstacle. It combines ideas due to Johansson and Sleeman [18] and Hettlich and Rundell [8] and reconstructs the obstacle from the far field pattern for scattering of one incident plane wave.     

Single-pion production in pp collisions at 0.95 GeV/c (I)

The single-pion production reactions pp → dπ⁺, pp → npπ⁺ and pp → ppπ⁰ were measured at a beam momentum of 0.95GeV/c ( T _p ≈ 400MeV) using the short version of the COSY-TOF spectrometer. The implementation of a central calorimeter provided particle identification, energy determination and neutron detection in addition to time-of-flight and angle measurements. Thus, all pion production channels were recorded with 1-4 overconstraints. The total and differential cross-sections obtained are compared to previous data and theoretical calculations. Main emphasis is put on the discussion of the ppπ⁰ channel, where we obtain angular distributions different from previous experimental results, however, partly in good agreement with recent phenomenological and theoretical predictions. In particular, we observe very large anisotropies for the π⁰ angular distributions in the kinematical region of small relative proton momenta revealing there a dominance of proton spinflip transitions associated with π⁰ s and d partial waves and emphasizing the important role of π⁰ d-waves.     

Multiseparability and superintegrability in three dimensions

In complex two-dimensional Euclidean space, the Hamilton-Jacobi or Schrödinger equation with a given “nondegenerate” potential is maximally superintegrable if and only if it is separated in more than one coordinate system. A similar statement for three dimensions is not known. In this paper, a start will be made on this problem by investigating the known separable Hamilton-Jacobi and Schrödinger systems to find those that are superintegrable.     

Raman scattering and electron-phonon coupling in mized-valent and superconducting compounds

Polarized Raman spectra of mixed-valent Sm_0.75Y_0.25S are presented and compared with those of semiconducting SmS and superconducting YS and TiN. The spectra are explained in terms of cluster deformabilities which also govern the phonon anomalies. The existence of a breathing Γ₁⁺ deformability of Sm in Sm_1?xY_xS, of S in YS, of N in TiN and a quadrupolar Γ₁₂⁺ deformability of N in TiN is demonstrated. The relationship between these results and the microscopic theory is discussed.     

Molecular dynamics simulations of compressed hydrogen

Abstract

Molecular dynamics simulations have been performed for highly compressed fluid hydrogen in the density and temperature regime of recent shock-compression experiments. Both density functional and tight-binding electronic structure techniques have been used to describe interatomic forces. Two tight-binding models of hydrogen have been developed with a single s-type orbital on each atom that reproduce properties of the dimer, of various crystalline structures, and of the fluid. The simulations indicate that the rapid rise in the electrical conductivity observed in the gas-gun experiments depends critically on the dissociated atoms (monomers). We find that the internal structure of warm, dense hydrogen has a pronounced time-dependent nature with the continual dissociation of molecules (dimers) and association of atoms (monomers). Finally, Hugoniots derived from the equations-of-state of these models do not exhibit the large compressions predicted by the recent laser experiments.