Imaging the domain pattern of the canted magnetization state in Co/Pt multilayer films

The exact magnetization pattern of magnetic films close to a spin-reorientation transition is difficult to analyze due to the intrinsically three-dimensional (3d) variation of the orientation of the local magnetization. We present a technique how this can be performed, based on the analysis of high quality 2d polarization maps from a single scanning electron microscope with polarization analysis (SEMPA) measurement with tilted sample. The key tool is the statistical distribution of all occurring polarization doublets, visualized in a 2d histogram plot. From the shape of the distribution the type of transition—canted-phase, or coexisting phases—can be inferred. For the canted-phase state, the canting angle can be accurately determined from geometrical considerations. With help of the histogram the image data can be analyzed and the three components of the magnetization can be calculated for most points of the image. For a Co/Pt multilayer film we found a cone state. The magnetization forms a complex pattern consisting of out-of-plane domains while the in-plane magnetization shows a maze pattern.     

Symbolic parametrization of curves

If algebraic varieties like curves or surfaces are to be manipulated by computers, it is essential to be able to represent these geometric objects in an appropriate way. For some applications an implicit representation by algebraic equations is desirable, whereas for others an explicit or parametric representation is more suitable. Therefore, transformation algorithms from one representation to the other are of utmost importance.We investigate the transformation of an implicit representation of a plane algebraic curve into a parametric representation. Various methods for computing a rational parametrization, if one exists, are described. As a new idea we introduce the concept of working with classes of conjugate (singular or simple) points on curves. All the necessary operations, like determining the multiplicity and the character of the singular points or passing a linear system of curves through these points, can be applied to such classes of conjugate points. Using this idea one can parametrize a curve if one knows only one simple point on it. We do not propose any new method for finding such a simple point. By classical methods a rational point on a rational curve can be computed, if such a point exists. Otherwise, one can express the coordinates of such a point in an algebraic extension of degree 2 over the ground field.     

Radiale Wärmeleitung in durchströmten Schüttungsrohren

Heat Transport to the Wall of Packed Tubes. Radial conduction of heat in packed tubes has a crucial influence on yield and selectivity of many heterogeneously catalyzed reactions. In spite of many years of intensive research in the field, there are still tremendous discrepancies between correlations of different origin. Even the standard model using two constant heat transport parameters, which was introduced in the fifties and has since become most widely accepted, has been controversially discussed and called into question. The unsatisfactory state of the art has been an incentive for several groups of researchers to take up this old topic once again. Three parallel experimental investigations on heat transport with air flowing in packed tubes of similar dimensions, electrically heated, steam-heated, or water-cooled, were completed in 1991. Comparative evaluation of the results of these three investigations, together with other data from the relevant literature, now provides the first clear answers to some of the questions so controversially discussed in the past.     

Autothermal two-stage gasification of low-density waste-derived fuels

In order to increase the efficiency of waste utilization in thermal conversion processes, pre-treatment is advantageous. With the Herhof Stabilat^® process, residual domestic waste is upgraded to waste-derived fuel by means of biological drying and mechanical separation of inerts and metals. The dried and homogenized waste-derived Stabilat^® fuel has a relatively high calorific value and contains high volatile matter which makes it suitable for gasification. As a result of extensive mechanical treatment, the Stabilat^® produced is of a fluffy appearance with a low density. A two-stage gasifier, based on a parallel-arranged bubbling fluidized bed and a fixed bed reactor, has been developed to convert Stabilat^® into hydrogen-rich product gas. This paper focuses on the design and construction of the configured laboratory-scale gasifier and experience with its operation. The processing of low-density fluffy waste-derived fuel using small-scale equipment demands special technical solutions for the core components as well as for the peripheral equipment. These are discussed here. The operating results of Stabilat^® gasification are also presented.