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     

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.     

On the Role of Physics in the Growth and Pattern Formation of Multi-Cellular Systems: What can we Learn from Individual-Cell Based Models?

We demonstrate that many collective phenomena in multi-cellular systems can be explained by models in which cells, despite their complexity, are represented as simple particles which are parameterized mainly by their physical properties. We mainly focus on two examples that nevertheless span a wide range of biological sub-disciplines: Unstructured cell populations growing in cell culture and growing cell layers in early animal development. While cultured unstructured cell populations would apriori been classified as particularly suited for a biophysical approach since the degree to which they are committed to a genetic program is expected to be modest, early animal development would be expected to mark the other extreme—here the degree of determinism according to a genetic program would be expected to be very high. We consider a number of phenomena such as the growth kinetics and spatial structure formation of monolayers and multicellular spheroids, the effect of the presence of another cell type surrounding the growing cell population, the effect of mutations and the critical surface dynamics of monolayers. Different from unstructured cell populations, cells in early development and at tissue interfaces usually form highly organized structures. An example are tissue layers. Under certain circumstances such layers are observed to fold. We show that folding pattern again can largely be explained by physical mechanisms either by a buckling instability or active cell shape changes. The paper combines new and published material and aims at an overview of a wide range of physical aspects in unstructured populations and growing tissue layers.     

New disc-shaped mesogens based on pentakis(phenylethynyl)benzene derivatives

First examples of amphiphilic alkyl pentakis(phenylethynyl)benzene ethers containing functional groups at the terminal position of their alkoxy chains were synthesized by etherification of pentabromophenol with 11-bromoundecan-1-ol and 11-bromoundecanoic acid ethyl ester, respectively, and subsequent palladium catalyzed, fivefold coupling reactions with the substituted phenylacetylene. Two undecanoic acid derivatives with different pentakis(phenylethynyl)phenoxy substituents in the ω-position were prepared by ester cleavage from the corresponding ethyl esters. The thermal behaviours of five penta-alkynes in their pure states, as well as of their charge transfer complexes formed from mixtures with 2,4,7-tri-nitrofluorenone, were examined.     

On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve

In comparison with direct measurements of unsaturated hydraulic conductivity, the methods of calculations from the moisture retention curve are attractive for their fast and simple use and low cost. These are the main reasons for their increasing use, mainly in spatial variability studies. On the other hand, it is known that their applicability is limited. The possibility of the use of the retention curve to indirectly determine hydraulic conductivities is analyzed as follows. The theoretical derivation of the relationK(h) – (h) is briefly discussed with regards to potential sources of inaccuracy. The sensitivity of the algorithm forK(h) calculation is studied as a response to possible inaccuracies in the retention curve determination. Conclusions about the usability of calculated hydraulic conductivities are drawn.     

XPS investigations of ink‐jet printed paper

Different ink‐jet printed paper materials were investigated using X‐ray photoelectron spectroscopy (XPS) yielding the elemental composition of the near‐surface region of the papers. We found significant differences with respect to the detected elements and their atomic concentrations in the different inks studied here. Two different groups of inks could be identified by means of a lower ratio of the O and C atomic concentrations and lower concentrations in specific trace elements like Mg, Na and Si. High‐resolution spectra of C 1s and O 1s core levels allowed a detailed determination of the chemical state of the respective elements. On the basis of a detailed deconvolution of these XPS signals, significant differences between all the investigated ink‐jet printed papers were found, thereby allowing their discrimination. The applicability of the measurements and, more generally, the XPS technique for forensic investigations of paper are discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

Cluster isobars for high-precision mass spectrometry

Doublet mass measurements of the isobars²⁸Si₃ and¹²C₇ are performed by use of a Penning trap mass spectrometer and the Fourier transform ion cyclotron resonance (FT-ICR). The carbon and silicon cluster ions are produced by laser ablation. Results of these preliminary measurements are presented.