Zur Konstruktion lokal kompakter Dicksonscher Fastkörper

Ohne ZusammenfassungAus dem Nachlaß. Für den Druck vorbereitet von Theo Grundhöfer (Tübingen) und Heinz Lüneburg (Kaiserslautern).     

Topological speed limits to network synchronization

We study collective synchronization of pulse-coupled oscillators interacting on asymmetric random networks. We demonstrate that random matrix theory can be used to accurately predict the speed of synchronization in such networks in dependence on the dynamical and network parameters. Furthermore, we show that the speed of synchronization is limited by the network connectivity and remains finite, even if the coupling strength becomes infinite. In addition, our results indicate that synchrony is robust under structural perturbations of the network dynamics.     

The reproducible acquisition of comparative liquid chromatography/tandem mass spectrometry data from complex biological samples

An in-depth study of the reproducibility of data acquired for comparative proteomics analysis using a prototype two-stage heated laminar flow chamber fitted to a commercial high-performance liquid chromatography/tandem mass spectrometry (HPLC/MS/MS) instrument was undertaken. The study is based on 24 replicate samples from four independent membrane preparations derived from two matched breast cancer cell lines. Variation and reproducibility in the data were evaluated at several levels highlighting the relative efficiency and variability of the acquisition routines used. Specifically, variation in the number and relative intensities of chromatographic peaks eluted from the LC column, precursor ion selection and sequence identification were evaluated. On average, approximately 6500 chromatographic peaks were generated for each acquisition with a corresponding coefficient of variance (CV) of less than 20%. Precursor ion selection and sequence identification averaged 1380 and 780 events per acquisition sample, respectively, with corresponding CVs of less than 10% for each. The reproducibility in the precursor ion selection was typically better than 60% between similar replicates. Using protein and peptide internal standards, it was found that the CV in retention time across the gradient between two acquisition pairs was typically less than 5%, whereas the average intensity ratio was 1.0 (expected) with a CV approaching 20%. An evaluation of the intensity ratios calculated from endogenous peptide sequences, identified across the acquisition set, indicated a CV of approximately 30%. Similarly, the CV associated with the top 1000 peptides indicated a mean and median of 28.4 and 26.95%. For a given acquisition pair it was also found that approximately 11% of the chromatographic peaks eluting from the column were linked to a sequence or identified. For these experiments, less than 10% of the peak pairs had absolute ratios greater than 2.0 and of those only approximately 10% had sequences linked to them. For each matched acquisition set on average 406 proteins were identified with a CV of less than 10%. Of the proteins that were identified approximately 30% had at least one predicted trans-membrane domain, indicating a four-fold increase over a crude homogenate sample with only minor enrichment. During these experiments it was found that the interface did not significantly alter the relative charge state distribution of ions, nor did it introduce significant interference from background ions. The interface was capable of 24-hour acquisition cycles.     

Long chaotic transients in complex networks

We show that long chaotic transients dominate the dynamics of randomly diluted networks of pulse-coupled oscillators. This contrasts with the rapid convergence towards limit cycle attractors found in networks of globally coupled units. The lengths of the transients strongly depend on the network connectivity and vary by several orders of magnitude, with maximum transient lengths at intermediate connectivities. The dynamics of the transients exhibit a novel form of robust synchronization. An approximation to the largest Lyapunov exponent characterizing the chaotic nature of the transient dynamics is calculated analytically.     

Specific recording kinetics as a general property of unconventional photorefractive media

We introduce a model for the kinetics of grating formation during holographic recording in optically excitable two-state systems. An unexpected characteristic time dependence of the diffraction efficiency is found. We show that it originates from a nonlinear transformation of the light interference pattern into a refractive-index profile. Our findings strongly resemble and explain by nature the experimental data of two-state systems in general, here represented by two examples: sodium nitroprusside and terbium gallium garnet.     

Femtosecond photomagnetic switching of spins in ferrimagnetic garnet films

We demonstrate that intense laser pulses can be used to directly control the spins in ferrimagnetic garnet films. Through an ultrafast and nonthermal photomagnetic effect the magnetocrystalline anisotropy is modified to create a new long-lived equilibrium orientation for the magnetization. Simultaneously, the magnetization is rotated into this new state by precession in a strong transient optically generated magnetic field. All take place within the 100 fs duration of a single laser pulse, thus demonstrating the feasibility of photomagnetic switching on the femtosecond time scale.     

Precise subnanometer control of the position of a macro object by light pressure

For the first time to the authors' knowledge, efficient control of the position of a macro object by coherent light was demonstrated. The minimal controllable mechanical displacement induced by the light pressure was 9 pm. No dependence of light pressure on wavelength in a broad wavelength range (405-1560 nm) was observed, as predicted by Maxwell's theory.     

Shot noise in chaotic cavities from action correlations

We consider universal shot noise in ballistic chaotic cavities from a semiclassical point of view and show that it is due to action correlations within certain groups of classical trajectories. Using quantum graphs as a model system, we sum these trajectories analytically and find agreement with random-matrix theory. Unlike all action correlations which have been considered before, the correlations relevant for shot noise involve four trajectories and do not depend on the presence of any symmetry.     

Sedimentation of DNA supercoils and bacterial nucleoids

The sedimentation of DNA supercoils and bacterial nucleoids is discussed in terms of an asymptotic expression for the size of branched supercoils exhibiting an excluded-volume effect between superhelical segments. A Kirkwood–Riseman approximation is adopted for the sedimentation coefficient. The theory predicts the sedimentation of DNA supercoils fairly well despite their relatively small size in current simulations and experiments. We introduce a crosslinked supercoil model for bacterial nucleoids that are known to contain a variety of adsorbed proteins. Sedimentation experiments of the 1970s are discussed.