Strongly confined quantum wire states in strained T-shaped GaAs/InAlAs structures

The confinement energy of T-shaped quantum wires (QWRs), which were fabricated by the cleaved edge overgrowth technique in a way that the QWRs form at the intersection of In_0.2Al_0.8As stressor layers and the overgrown (1 1 0) GaAs quantum well (QW), is examined using micro-photoluminescence spectroscopy. Photoluminescence (PL) signals from individual QWRs can be spatially resolved, since the strained films are separated by 1 μm wide Al_0.3Ga_0.7As layers. We find that due to the tensile strain being transmitted to the QW, the confinement energy of the QWRs rises systematically up to 40 meV with increasing thickness of the stressor layers. By reducing the excitation power to 0.1 μW the QWR PL emission occurs 48 meV redshifted with respect to the QW. All QWR peaks exhibit smooth lineshapes, indicating the absence of pronounced exciton localization.     

Of Dogs and Fleas: The Dynamics of N Uncoupled Two-State Systems

The historical Ehrenfest model dating back to 1907 describes the process of equilibration together with fluctuations around the thermal equilibrium. This approach represents a special case in the dynamics of N uncoupled two-state systems. In this article we present a generalization of the original model by introducing an additional parameter p which denotes the probability of a single state change. Analytical solutions for the probability distribution of the system's state as well as the fluctuation distribution are derived. Interestingly, close inspection of the fluctuation distribution reveals an intrinsic time scale. Sampling the system's state at much slower rates yields the familiar macroscopic exponential distribution for equilibrium processes. For faster measurements a power law extends roughly over log₁₀ N orders of magnitude followed by an exponential tail. At some point, further increases of the sampling rate merely result in a shift of the fluctuation distribution towards higher values leaving plateau at small fluctuation sizes behind. Since the generic solution is rather unwieldy, we derive and discuss simple and intuitive analytical solutions in the limit of small p and large N. Furthermore, we relax the quantization of time by considering a complementary approach in continuous time. Finally we demonstrate that the fluctuation distributions resulting from the two different approaches bear identical characteristic features.     

Photopolymers for Rapid Prototyping of Soluble Mold Materials and Molding of Cellular Biomaterials

To substitute cross-linked photopolymers in rapid prototyping of mold materials and therefore extend the range of materials which can be casted, organo-soluble photopolymers were developed. Branched bisalkylacrylamides were suitable as base component for such formulations, due to their high reactivity, good mechanical properties, and excellent solubility of the formed polymers. These molding materials were used to prepare cellular biocompatible materials which could be used as bone replacement materials. Biocompatible crosslinkers based on methacrylates from hydrolyzed gelatine or lactic acid ethyleneglycol blockcopolymers and commercially available reactive diluents are the base components of such a formulation. Biocompatibility was investigated by osteoblast-like cells. Cellular biocompatible parts were obtained by thermal polymerization in soluble mould materials prepared by 3D-photoshaping.     

The maximum principle for the Bergman space and the Möbius pseudodistance for the annulus

It is shown that the formula for the Möbius pseudodistance for the annulus yields better estimates than previously known for the constant in the Bergman space maximum principle.

     

Estimating the strength of chaos from the power spectrum

It is rigorously proved that for nonlinear dynamical systems whose time dependence is described by one dimensional, everywhere expanding maps, the width of broadband noise in the power spectrum is bounded by the generalized entropiesK ₂ andK ₃, which measure the strength of chaos in this system asK ₂2K ₃.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Investigation of the formation process of MCs+-molecular ions during sputtering

In secondary ion mass spectrometry, the detection of MCs+ clusters (with M an element of the specimen) under a Cs bombardment is frequently used for the quantification of major elements. Despite some very good results obtained by this method, some problems still remain. In order to gain some more insight into these problems, the formation mechanism of the MCs+ clusters is investigated using a Monte Carlo model. It is shown that the majority of the constituent particles of the formed clusters are initially first or second neighbor atoms at the surface and that the velocity distribution of the MCs+ clusters becomes broader and peaked at higher velocities with increasing surface binding energy of the M atom. In addition, it is demonstrated that the interaction potential between the M and Cs+ particle has no influence on the velocity distribution of the MCs+ clusters. On the other hand, the cluster formation probability, defined as the probability that a sputtered M and Cs+ particle will form a MCs+ cluster, is extremely sensitive to this interaction potential. It is also shown that the cluster formation probability decreases with increasing surface binding energy. Finally, a good correspondence is obtained between the calculated and experimental velocity distributions of MCs+ clusters sputtered from different monoatomic materials. As a consequence, the Monte Carlo model and the discussed results can be validated.     

Multipole expansion of diatomic overlap

A systematic extension of Ruedenberg's expansion formula is applied to evaluate two-electron integrals occurring in calculations on molecular structure. Minimum STO basis sets are used for all SCF-calculations within the framework of the MEDO-method (Multipole Expansion of Diatomic Overlap). The errors due to this approximation scheme are almost negligible compared to those introduced by the truncated basis set: LiH, Li₂ and N₂ are chosen as examples.     

High facial diastereoselectivity in intra- and intermolecular reactions of chiral benzylic cations

Chiral carbenium ions can be attacked by arene nucleophiles with high facial diastereoselectivity (dr >/= 94/6). Benzylic cations, such as 2, were generated under acidic conditions and reacted with arenes in intra- and intermolecular Friedel-Crafts alkylation reaction. The depicted reaction 1 --> 3 represents one example for the unprecedented, highly diastereoselective intermolecular Friedel-Crafts alkylation reactions which were observed in this study.