Cardy's Formula for Certain Models of the Bond-Triangular Type

We introduce and study a family of 2D percolation systems which are based on the bond percolation model of the triangular lattice. The system under study has local correlations, however, bonds separated by a few lattice spacings act independently of one another. By avoiding explicit use of microscopic paths, it is first established that the model possesses the typical attributes which are indicative of critical behavior in 2D percolation problems. Subsequently, the so called Cardy-Carleson functions are demonstrated to satisfy, in the continuum limit, Cardy's formula for crossing probabilities. This extends the results of S. Smirnov to a non-trivial class of critical 2D percolation systems.Comment: 49 pages, 7 figure

Ree geometries

We introduce a rank 3 geometry for any Ree group over a not necessarily perfect field and show that its full collineation group is the automorphism group of the corresponding Ree group. A similar result holds for two rank 2 geometries obtained as a truncation of this rank 3 geometry. As an application, we show that a polarity in any Moufang generalized hexagon is unambiguously determined by its set of absolute points, or equivalently, its set of absolute lines

Groups of Lie type generated by long root elements in F4(K)

AbstractLet K be a field and G a quasi-simple subgroup of the Chevalley group F4(K). We assume that G is generated by a class Σ of abstract root subgroups such that there are A,C∈Σ with [A,C]∈Σ and any A∈Σ is contained in a long root subgroup of F4(K). We determine the possibilities for G and describe the embedding of G in F4(K)

Mssbauer study of Се2Fe17 compound in different magnetic states

Mssbauer spectra of two samples of the Ce2Fe17 compound have been analyzed and hyperfine parameters, compared. The samples were subjected to different preparation techniques and display different magnetic properties. It is established that to well fit the Mssbauer spectra of these samples, an appropriate model should be used that takes into account an additional subspectrum differing in hyperfine parameters from the subspectra employed in conventional models. It is shown that in the ferromagnetic state, the samples contain local regions with an antiferromagnetic order, the volume fraction of which, being different for two samples, increases on approaching the temperature of ferro-to-antiferromagnet transition

Supramolecular assembly, chirality, and electronic properties of rubrene studied by STM and STS

This thesis presents the first experimental results of a scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) investigation of rubrene at the supramolecular, molecular and submolecular level. Based on its semiconducting and fluorescent properties, this molecule is of particular interest in view of the emerging fields of molecular electronics and optoelectronics which could one day replace the conventional technology relying on semiconductors such as silicon and gallium arsenide. The goal is the substitution of these inorganic materials by cheap and flexible layers of semiconducting organic molecules for a new class of diodes and transistors, as well as the realization of electronic switches based on individual molecules. One fundamental approach is to take advantage of the molecular self-assembly behavior which results in the creation of well-ordered supramolecular structures. The investigations of the self-assembly of rubrene adsorbed on metal surfaces (Au(111), Au(100), Ag(111), and Ag(100)), which were carried out within the framework of this thesis, show a surprising diversity of supramolecular structures. Amongst other shapes, the molecules organize themselves into geometries of perfect hexagonal and pentagonal symmetry and create multifaceted patterns on the surface. A fascinating peculiarity consists in the spontaneous construction of nested structures which are built up by a hierarchical self-assembly of individual molecules into pentagonal supermolecules which form in a second step perfect supramolecular decagons. The geometric shape of rubrene is characterized by a structural asymmetry leading to the existence of two mirror imaged versions of the molecule which are not superimposable to each other, such as for instance our left and right hand or the helical DNA. The aspect of chirality is crucial for basic processes in living systems and calls for a fundamental understanding of the interaction mechanisms occurring between chiral molecules. The experiments on rubrene reveal that the intermolecular bonding differentiates between the two chiral types of the molecule (chiral recognition), yielding the self-organization into homochiral structures. These assemblies exhibit a geometry which is again chiral, demonstrating a propagation of chirality throughout the three stages of the supramolecular hierarchy. The semiconducting behavior of rubrene is furthermore probed by STS measurements detecting the energetic positions of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). The experimental data uncover that different adsorption conformations exhibit characteristic HOMO energies and reveal adsorption conformations of rubrene which preserve the intrinsic electronic structure of the free molecule. Furthermore, a switching of the molecular conformation and the electronic structure of one rubrene conformer is induced with the STM