Continuity for self-destructive percolation in the plane

A few years ago two of us introduced, motivated by the study of certain forest-fireprocesses, the self-destructive percolation model (abbreviated as sdp model). A typical configuration for the sdp model with parameters p and delta is generated in three steps: First we generate a typical configuration for the ordinary percolation model with parameter p. Next, we make all sites in the infinite occupied cluster vacant. Finally, each site that was already vacant in the beginning or made vacant by the above action, becomes occupied with probability delta (independent of the other sites). Let theta(p, delta) be the probability that some specified vertex belongs, in the final configuration, to an infinite occupied cluster. In our earlier paper we stated the conjecture that, for the square lattice and other planar lattices, the function theta has a discontinuity at points of the form (p_c, delta), with delta sufficiently small. We also showed remarkable consequences for the forest-fire models. The conjecture naturally raises the question whether the function theta is continuous outside some region of the above mentioned form. We prove that this is indeed the case. An important ingredient in our proof is a (somewhat stronger form of a) recent ingenious RSW-like percolation result of Bollob\'{a}s and Riordan

Deep drawing simulation of Tailored Blanks

Tailored blanks are increasingly used in the automotive industry. A tailored blank consists of different metal parts, which are joined by a welding process. These metal parts usually have different material properties. Hence, the main advantage of using a tailored blank is to provide the right material properties at specific parts of the blank. The movement of the weld during forming is extremely important. Unwanted weld displacement can cause damage to both the product and the tool. This depends mainly on the original weld position and the process parameters. However experimental determination of the optimum weld position is quite expensive. Therefore a numerical tool has been developed for simulations of tailored blank forming. The Finite Element Code Dieka is used for the deep drawing simulations of some geometrically simple products. The results have been validated by comparing them with experimental data and show a satisfactory correlation

On the abelianization of the Torelli group

Around 1980 Dennis Johnson computed the abelianized Torelli group for surfaces of genus at least three and at most one boundary component. His computation shows that it is completely described in terms of the first homology group of the surface. We show in this thesis that this result holds for all surfaces with boundary and genus at least three. Our method differs from his, is inductive in nature and may open the way to compute also higher homology groups of the Torelli group. Further, we compute the Torelli group for low genus in some cases, using the result of Mess for genus two

Observation of anomalous Hanle spin precession lineshapes resulting from interaction with localized states

It has been shown recently that in spin precession experiments, the interaction of spins with localized states can change the response to a magnetic field, leading to a modified, effective spin relaxation time and precession frequency. Here, we show that also the shape of the Hanle curve can change, so that it cannot be fitted with the solutions of the conventional Bloch equation. We present experimental data that shows such an effect arising at low temperatures in epitaxial graphene on silicon carbide with localized states in the carbon buffer layer. We compare the strength of the effect between materials with different growth methods, epitaxial growth by sublimation and by chemical vapor deposition. The presented analysis gives information about the density of localized states and their coupling to the graphene states, which is inaccessible by charge transport measurements and can be applied to any spin transport channel that is coupled to localized states.Comment: 6 pages, 6 figure