Positive and negative results concerning the Gromov-Lawson-Rosenberg conjecture

The Gromov-Lawson-Rosenberg-conjecture for a group G states that a closed spin manifold M^n (n>4) with fundamental group G admits a metric with positive scalar curvature if and only if its C^*-index A(M) in KO_n(C^*_r(G)) vanishes. We prove this for groups G with low-dimensional classifying space, provided the assembly map for G is injective. On the other hand, we construct a spin manifold with no metric with scal>0 but so that already its KO-orientation in KO_*(B pi_1(M)) vanishes. Therefore a corresponding weakened version or the GLR-conjecture is wrong. Last we address non-orientable manifolds. We give a reformulation of the minimal surface method of Schoen and Yau (extended to dimension 8) and introduce a non-orientable version of it. We then construct a manifold M whose orientation cover admits a metric of positive scalar curvature but where M itself does not. M is also a counterexample to a twisted analog of the GLR-conjecture because its twisted index vanishes.Comment: References corrected, AMS-LaTeX2e, 20 page

Defects in Lamellar Diblock Copolymers: Chevron- and Omega-shaped Tilt Boundaries

We investigate symmetric grain boundaries in a lamellar diblock copolymer system. The form of the interface between two grains strongly depends on the angle $\theta$, between the normals of the grains. When this angle is small, the lamellae transform smoothly from one orientation to the other, creating the chevron morphology. As $\theta$ increases, a gradual transition is observed to an omega morphology characterized by a protrusion of the lamellae along the interface between the two phases. We present a theoretical approach to find these tilt boundaries in two-dimensional systems, based on a Ginzburg-Landau expansion of the free energy. Calculated order parameter profiles and energies agree well with transmission electron microscope experiments, and with full numerical solution of the same problem.Comment: 11 pages, 10 gzipped postscript and jpeg figures, published in PRE Vol. 61, March 200

Ferromagnetism in Two Dimensions- Some Models and Applications

Paper by Michael Schic

Ionic effects on the electric field needed to orient dielectric lamellae

We consider the effect of mobile ions on the applied potential needed to reorient a lamellar system of two different materials placed between two planar electrodes. The reorientation occurs from a configuration parallel to the electrodes favored by surface interactions to an orientation perpendicular to the electrodes favored by the electric field. The system consists of alternating A and B layers with different dielectric constants. The mobile ions are assumed to be insoluble in the B layers and hence confined to the A layers. We find that the ions reduce the needed voltage most strongly when they are constrained such that each A lamella is electrically neutral. In this case, a macroscopic separation of charge and its concomitant lowering of free energy, is attained only in the perpendicular orientation. When the ions are free to move between different A layers, such that charge neutrality is only required globally, their effect is smaller and depends upon the preferred surface interaction of the two materials. Under some conditions, the addition of ions can actually stabilize the parallel configuration. Our predictions are relevant to recent experiments conducted on lamellar phases of diblock copolymer films with ionic selective impurities.Comment: To be published in the Journal of Chemical Physic

Nach der Krise: Wirksame Regelungen auf dem Finanzmarkt?

Schon während der Krise hat auf allen politischen Ebenen eine lebhafte Diskussion über eine bessere Finanzmarktregulierung eingesetzt. Einig war man sich nur in wenigen Bereichen. Und von der Umsetzung etwaiger Reformen ist die Politik noch weit entfernt. Allerdings ist auch fraglich, ob die Ansatzpunkte überhaupt richtig gewählt sind

Advances in friction stir welding by separate control of shoulder and probe

Friction stir welding (FSW) has developed into a reliable and increasing used industrial joining technology. Various tool configurations can be used for FSW, each of which has advantages and challenges. State-of-the-art FSW employs various tool configurations, including the conventional, the stationary shoulder, and the dual-rotational configuration which is characterized by separate control of shoulder and probe. In this study, an innovative method to combine various tool configurations was developed by a novel FSW spindle stack construction. With an additional servomotor, existing FSW systems can be extended by separate control of shoulder and probe so that varying rotational speeds and rotational directions can be set. This allows enhanced possibilities (a) to adjust frictional heat generation and (b) to apply several tool configurations. The main advantages of this enhanced type of FSW are demonstrated in three ways: increased weld penetration depth, reduction of undesirable machine vibrations, and the combination of varying tool configurations such as stationary shoulder and conventional FSW. The investigations were carried out with 2-mm EN AA 5754 H22 sheets and performed on a robotized FSW setup