Buchbesprechungen

Ohne Zusammenfassung     

A variational proof of the Gauss-Bonnet formula

The classical Gauss-Bonnet formula has the form I(g_ij)=2, where I(g_ij) represents a sum of three terms each of which depends on the metric tensor g_ij. It is shown that the first variation I of I(g_ij) with respect to the metric g_ij vanishes and that for the Euclidean metric _ij we have I(_ij)=2. From this the formula I(g_ij)=2 follows. In the process, explicit expressions are obtained for the first variation of each of the three terms which comprise I(g_ij). Furthermore, a general expression for the first variation of a multiple integral whose integrand is a scalar density depending on the metric tensor g_ij and its derivatives up to the second order is obtained with the aid of results of Rund [1].     

Flanking transmission of metal stud walls with different junction details

Measurements of the normalised flanking sound level difference of different gypsum board flanking walls are reported. Results of a “standard” wall construction confirmed some results of the current draft standard of DIN 4109. Different constructions with various junction details and different wall constructions are described and measurement results are presented. By additional measurements on the walls, a prediction model for the weighted flanking level difference is suggested, based on the methodology of EN 12354. For the flanking transmission prediction of path Ff, three transmission paths are proposed. The model gives good agreement between calculated and measured weighted flanking level difference except for the case where the transmission along the inner lining of the flanking wall is dominant. In this case the prediction underestimates measurements by up to 7 dB.     

Heat Content Asymptotics for Oblique Boundary Conditions

We consider the short-time heat content asymptotics for oblique boundary conditions. The first few coefficients in the asymptotic expansion are calculated.     

Interlayer coupling between out-of-plane magnetized multilayers across a thin antiferromagnetic spacer

The interlayer exchange coupling between Co/Pt perpendicular-to-plane magnetized layers across a thin IrMn spacer layer was experimentally studied. In contrast to earlier studies on interlayer coupling through antiferromagnetic NiO, which revealed an oscillatory coupling behavior as a function of NiO thickness, a ferromagnetic coupling was observed here in the range of IrMn thickness between 0.6 and 1.5 nm and antiferromagnetic between 1.5 and 2.5 nm. The antiferromagnetic coupling is attributed to an orange peel magnetostatic mechanism whereas the ferromagnetic coupling is attributed to an out-of-plane polarization of the antiferromagnetic IrMn layer induced by the interfacial exchange interaction with the adjacent out-of-plane ferromagnetic layers. Measurements of hysteresis loops versus temperature show that the coupling vanishes at 510 K for t_IrMn=1 nm. This critical temperature is far below the Néel temperature of bulk IrMn, but above the blocking temperature of IrMn/Co bilayers at such thickness. Using a one-dimensional model describing a partial domain wall in the antiferromagnet, we explain the coupling in terms of an out-of-plane tilt of the Mn moments at the IrMn/(Co/Pt) interfaces yielding a weak net polarization of the IrMn. Finally, the non-oscillatory decay of the coupling was attributed to the compensated spin structure of the IrMn in the parallel to the interfaces.     

On the stability of Archimedean tilings formed by patchy particles

We have investigated the possibility of decorating, using a bottom-up strategy, patchy particles in such a way that they self-assemble in (two-dimensional) Archimedean tilings. Except for the trihexagonal tiling, we have identified conditions under which this is indeed possible. The more compact tilings, i.e., the elongated triangular and the snub square tilings (which are built up by triangles and squares only) are found to be stable up to intermediate pressure values in the vertex representation, i.e., where the tiling is decorated with particles at its vertices. The other tilings, which are built up by rather large hexagons, octagons and dodecagons, are stable over a relatively large pressure range in the centre representation where the particles occupy the centres of the polygonal units.     

The decomposition numbers of Hecke algebras of typeF 4 with unequal parameters

The purpose of this paper is to calculate the decomposition numbers for Hecke algebras of typeF ₄ (andC ₃) with unequal parameters. The problem is reduced to specifying decomposition maps of the generic Hecke algebras. The concept of Kazhdan-Lusztig polynomials and left cells serves to determine their irreducible representations. We also prove a result about the minimal ring over which the irreducible representations of the generic algebras can be realized.