Hopf Algebras, Renormalization and Noncommutative Geometry

We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of tranverse index theory for foliations. Received: 14 August 1998/ Accepted: 5 October 1998     

On the Photophysical Properties of New Luminol Derivatives and their Synthetic Phthalimide Precursors

The photophysical properties of a series of structurally related 4-aminophthalimides and the corresponding 5-aminophthalic hydrazides (luminols) are reported. Absorption, steady-state, and time-resolved fluorescence spectra of luminols exhibited substitution, solvent, and pH dependence. Singlet lifetimes have been determined by time-resolved laser flash spectroscopy. UV spectra in gas phase and DMSO solution were calculated by TD-DFT which revealed the existence of two low-energy excited singlet states with strong pH-sensitivity.     

Development of a time-resolved white-light interference microscope for optical phase measurements during fs-laser material processing

A modified Mach–Zehnder interferometer set-up combined with microscope objectives has been developed for the measurement of phase changes in the processed material sample, like modification and melting of glass. The white light is generated by focusing ultrafast laser radiation (t _p=80 fs) in a sapphire crystal using a micro-lens array to minimize temporal and spatial fluctuations in the white-light continuum. Lateral and coaxial pump-probe measurements of the phase changes during material processing are performed using two coupled ultrafast laser sources at different repetition rates (f _rep=1 Hz–1 MHz). The optical phase shift and therefore the refractive index of the material are calculated from the interference images using two approaches. The knowledge of the refractive index during the laser processing with a temporal resolution in the ps-range and a spatial resolution of several microns leads to a better understanding of the initial processes for the permanent material modifications.     

Single-server queues with spatially distributed arrivals

Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server's movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The service times are independent, but arbitrarily distributed. The model generalizes the continuous cyclic polling system (the diffusion coefficient of the Brownian motion is zero in this case) and can be interpreted as a continuous version of a Markov polling system. Using Tweedie's lemma for positive recurrence of Markov chains with general state space, we show that the system is stable if and only if the traffic intensity is less than one. Moreover, we derive a stochastic decomposition result which leads to equilibrium equations for the stationary configuration of customers on the circle. Steady-state performance characteristics are determined, in particular the expected number of customers in the system as seen by a travelling server and at an arbitrary point in time.     

Anatomy of a gauge theory

We exhibit the role of Hochschild cohomology in quantum field theory with particular emphasis on gauge theory and Dyson–Schwinger equations, the quantum equations of motion. These equations emerge from Hopf- and Lie algebra theory and free quantum field theory only. In the course of our analysis, we exhibit an intimate relation between the Slavnov–Taylor identities for the couplings and the existence of Hopf sub-algebras defined on the sum of all graphs at a given loop order, surpassing the need to work on single diagrams.     

Purkinje imaging system to measure anterior segment scattering in the human eye

We present an instrument based on Purkinje imaging that permits the objective measurement of the amount of scattering associated with the eye's anterior segment, avoiding the contribution from the retina. The experimental system records the fourth Purkinje image, and adequate processing is used to compute a parameter that quantifies the scattering. The method was first tested in an artificial eye and later in normal young eyes wearing customized contact lenses that induced different amounts of scatter. We were able to detect scattering increments, which indicates that this technique may be used as an objective tool to quantify the level of scattering in the anterior segment of the living human eye. The future use of this technique in clinical environments might help to estimate the level of corneal haze in eyes undergoing refractive surgery or/and scattering within the lens during cataract development.     

Generation of hard X-ray radiation using the triboelectric effect by peeling adhesive tape

The triboelectric effect describes electrical charging when bringing different materials into contact. We report on the generation of hard X-ray radiation by peeling various adhesive tapes under medium vacuum conditions. Beside vacuum housing and pumps as instrumentation only an electric motor, two rolls and a metal foil as target material are necessary. The spectral distribution of generated X-rays was analyzed using an energy-dispersive detector. Depending on peeling speed, pressure and choice of material combination, electrons with energies sufficient to excite emission in the hard X-ray region are produced. The results are discussed in terms of triboelectric separation of charge carriers.     

The materials science X‐ray beamline BL8 at the DELTA storage ring

The hard X‐ray beamline BL8 at the superconducting asymmetric wiggler at the 1.5 GeV Dortmund Electron Accelerator DELTA is described. This beamline is dedicated to X‐ray studies in the spectral range from ～1 keV to ～25 keV photon energy. The monochromator as well as the other optical components of the beamline are optimized accordingly. The endstation comprises a six‐axis diffractometer that is capable of carrying heavy loads related to non‐ambient sample environments such as, for example, ultrahigh‐vacuum systems, high‐pressure cells or liquid‐helium cryostats. X‐ray absorption spectra from several reference compounds illustrate the performance. Besides transmission measurements, fluorescence detection for dilute sample systems as well as surface‐sensitive reflection‐mode experiments have been performed. The results show that high‐quality EXAFS data can be obtained in the quick‐scanning EXAFS mode within a few seconds of acquisition time, enabling time‐resolved in situ experiments using standard beamline equipment that is permanently available. The performance of the new beamline, especially in terms of the photon flux and energy resolution, is competitive with other insertion‐device beamlines worldwide, and several sophisticated experiments including surface‐sensitive EXAFS experiments are feasible.