Scattering loss in Nd-doped silica based optical fibers

Rare-earth doped fibers suffer from relatively high attenuation in comparison to conventional communication fibers. In order to improve the properties of such fibers, understanding of the mechanisms involved in scattering effects is of great importance. The effect of Nd-doping, Al-codoping and of the drawing temperature on the scattering effect was investigated for several different optical fibers. To this end a measuring setup was realized which allows absolute measurements of the scattering coefficient at different positions along a fiber. Also separation of total attenuation and scattering effects is possible. The presented results indicate scattering effects as primary source for increased attenuation compared with undoped fibers.     

Chemometric investigations on the representativity of soil sampling

Summary The characterization of the heavy metal contents of a soil area is carried out by narrow screening sampling and subsequent analysis. It is possible by means of the univariate variance analysis to detect significant alterations within the tested area. The position and extent of multivariate changes of the features can be characterized more exactly with the help of multivariate statistical methods such as the combination of cluster and discriminant analytical methods or the principal component analysis. The maximum possible distance between two sampling points is determined by calculation of the autocorrelation function of the features. The number of soil samples, which is necessary for precisely determining the heavy metal contents of the investigated area, can be derived therefrom. With the help of the multivariate autocorrelation function the distance for the representative sampling of the multivariate loads by heavy metals can be described.     

Asymptotic behavior of positive solution branches of elliptic problems with linear part at resonance

We consider Dirichlet problems for semilinear elliptic equations whose linear part is at resonance. For various types of nonlinearities we provide sufficient conditions for the solvability of these problems for certain types of forcing terms. Depending upon the dimension of the independent variable and the shape of the domain, we obtain multiple existence results and show that in some cases infinitely many solutions may exist.Dedicated to Klaus Kirchgässner on the occasion of his 60th birthdayThe authors' work on this project has been supported by several institutions and thanks are due to the University of Utah for granting Schaaf a one year's visiting professorship during 1989–1990, to the DFG and the University of Stuttgart for providing Schmitt with the opportunity to visit that institution during the summer semester 1989. Final preparation was supported by a grant from NSF.     

The optimal size of the exchange hole and reduction to one-particle Hamiltonians

We use the concept of the exchange hole introduced by Slater to bound the energy of atoms, molecules, and other systems interacting by Coulomb forces from below by one-particle Hamiltonians with an effective screening potential and an exchange hole around each electron. Interestingly enough the optimal size of the exchange hole is smaller than Slater proposed: the best lower bound is obtained when the exchange hole carries charge 1/2 instead of 1. To highlight the quality of our estimate we show that the Dirac exchange energy with a slightly different constant bounds the exchange–correlation energy from below, an estimate previously derived by Lieb and later improved by Lieb and Oxford. Acknowledgements The authors thank Walter Farkas and Christian Hainzl for helpful discussions. Financial support by the European Union under its IHP network program, grant HPRN-CT-2002-00277, is gratefully acknowledged.© By the authorsThe author A.M. Klaus Müller is deceased     

Some historical and technical aspects of beam quality

A survey is given on the various algorithms to describe the propagation of radiation fields in the paraxial approximation, starting with the Kirchhoff-Fresnel-Collins-integral and ending with the intensity moments and the generalizedABCD-law. The importance of characterizing beam quality for technical applications by suitable parameters is pointed out. The two competing definitions of beam parameters, intensity moments and power content values are discussed.