Curvature coupling dependence of membrane protein diffusion coefficients

We consider the lateral diffusion of a protein interacting with the curvature of the membrane. The interaction energy is minimized if the particle is at a membrane position with a certain curvature that agrees with the spontaneous curvature of the particle. We employ stochastic simulations that take into account both the thermal fluctuations of the membrane and the diffusive behavior of the particle. In this study, we neglect the influence of the particle on the membrane dynamics, thus the membrane dynamics agrees with that of a freely fluctuating membrane. Overall, we find that this curvature coupling substantially enhances the diffusion coefficient. We compare the ratio of the projected or measured diffusion coefficient and the free intramembrane diffusion coefficient, which is a parameter of the simulations, with analytical results that rely on several approximations. We find that the simulations always lead to a somewhat smaller diffusion coefficient than that from our analytical approach. A detailed study of the correlations of the forces acting on the particle indicates that the diffusing inclusion tries to follow favorable positions on the membrane such that forces along the trajectory are on average smaller than they would be for random particle positions.     

Pascal's Theorem and Quantum Deformation

By a transfer principle, Pascal's Theorem is equivalent to a theorem about point pairs on the real line. It appears that Pascal's Theorem is equivalent to the vanishing of a common invariant of six quadratic forms. Using the q-deformed invariant theory of Leitenberger (J. Algebra 222 (1999), 82), we construct corresponding quantum invariants by a computer calculation.     

Abel’s theorem in the noncommutative case

We define noncommutative binary forms. Using the typical representation of Hermite we prove the fundamental theorem of algebra and we derive a noncommutative Cardano formula for cubic forms. We define quantized elliptic and hyperelliptic differentials of the first kind. Following Abel we prove Abel’s theorem.     

Strain relaxation and vacancy creation in thin platinum films

Synchrotron based combined in situ x-ray diffractometry and reflectometry is used to investigate the role of vacancies for the relaxation of residual stress in thin metallic Pt films. From the experimentally determined relative changes of the lattice parameter a and of the film thickness L the modification of vacancy concentration and residual strain was derived as a function of annealing time at 130 °C. The results indicate that relaxation of strain resulting from compressive stress is accompanied by the creation of vacancies at the free film surface. This proves experimentally the postulated dominant role of vacancies for stress relaxation in thin metal films close to room temperature.     

Application of a pnCCD in X‐ray diffraction: a three‐dimensional X‐ray detector

The first application of a pnCCD detector for X‐ray scattering experiments using white synchrotron radiation at BESSY II is presented. A Cd arachidate multilayer was investigated in reflection geometry within the energy range 7 keV < E < 35 keV. At fixed angle of incidence the two‐dimensional diffraction pattern containing several multilayer Bragg peaks and respective diffuse‐resonant Bragg sheets were observed. Since every pixel of the detector is able to determine the energy of every incoming photon with a resolution ΔE/E? 10^?2, a three‐dimensional dataset is finally obtained. In order to achieve this energy resolution the detector was operated in the so‐called single‐photon‐counting mode. A full dataset was evaluated taking into account all photons recorded within 10⁵ detector frames at a readout rate of 200 Hz. By representing the data in reciprocal‐space coordinates, it becomes obvious that this experiment with the pnCCD detector provides the same information as that obtained by combining a large number of monochromatic scattering experiments using conventional area detectors.     

A quantum deformation of invariants of binary forms

The modern representation theory has its roots in the classical theory of invariants of binary forms of Caley, Silvester, Clebsch, Gordan, Capelli etc. We use the theory of the quantum group U _q(sl(2, IR) in order to develop a quantum theory of invariants. Higher binary forms are introduced on the basis of braided algebras. We define quantised invariants and give basic examples. We show that the symbolic method of Clebsch and Gordan works also in the quantised case. We calculate the quantised discriminant of the quadratic form, the quantised catalecticant of the quartic form and further invariants without a classical analogon.     

Optimized spatial overlap in optical pump–X‐ray probe experiments with high repetition rate using laser‐induced surface distortions

Ultrafast X‐ray diffraction experiments require careful adjustment of the spatial overlap between the optical excitation and the X‐ray probe pulse. This is especially challenging at high laser repetition rates. Sample distortions caused by the large heat load on the sample and the relatively low optical energy per pulse lead to only tiny signal changes. In consequence, this results in small footprints of the optical excitation on the sample, which turns the adjustment of the overlap difficult. Here a method for reliable overlap adjustment based on reciprocal space mapping of a laser excited thin film is presented.     

Structural characterization of a spin-assisted colloid-polyelectrolyte assembly: stratified multilayer thin films

The assembly of polyelectrolytes and gold nanoparticles yields stratified multilayers with very low roughness and high structural perfection. The films are prepared by spin-assisted layer-by-layer self-assembly (LbL) and are characterized by X-ray reflectivity (XRR), UV-vis spectroscopy, atomic force microscopy (AFM), and transmission electron microscopy (TEM). Typical structures have four repeat units, each of which consists of eight double layers (DL) of poly(sodium 4-styrenesulfonate)/poly(allylamine hydrochloride), one monolayer of gold nanoparticles (10 nm diameter), and another layer of poly(allylamine hydrochloride). XRR scans show small-angle Bragg peaks up to seventh order, evidencing the highly stratified structure. Pronounced Kiessig fringes indicate a low global roughness, which is confirmed by local AFM measurements. TEM images corroborate the layered structure in the growth direction and nicely show the distinct separation of the individual particle layers. An AFM study reveals the lateral gold particle distribution within one individual particle layer. Interestingly, the spin-assisted deposition of polyelectrolytes reduces the roughness induced by the particle layers, leading to self-healing of roughness defects and a rather perfect stratification.