Cogenerators for convex spaces

We give cogenerators for the categories of convex (= finitely superconvex), finitely positively convex, and absolute convex (= finitely totally convex) spaces introduced by Pumplün and Röhrl.Dedicated to our academic teacher Dieter Pumplün on the occasion of his sixtieth birthday.     

Covariance estimation under spatial dependence

Correlated multivariate processes have a dependence structure which must be taken into account when estimating the covariance matrix. The natural estimator of the covariance matrix is introduced and is shown that to be biased under the dependence structure. This bias is studied under two different asymptotic models, namely increasing the domain by increasing the number of observations, and increasing the number of observations in the fixed domain. Using the first asymptotic model, we quantify the convergence rate of the bias and of the covariance between the components of the estimated covariance matrix. The second asymptotic model serves to derive a fast and accurate bias correction. As shown, under mild hypotheses, the asymptotic normality of the estimated covariance matrix holds and can be used to test whether the bias is significant, for example, in the sense that the eigenvectors of the estimated and true covariance matrices are significantly different.     

Time-domain simulations of sound propagation through screen-induced turbulence

A flow model in combination with a statistical-dynamical turbulence generator and a linearised Euler time-domain model for sound waves were used to simulate the effect of screen-induced turbulence on the noise level in the acoustical shadow of a screen in wind. Instead of simulating a great number of different frozen turbulence realisations, the concept of transient turbulence was successfully tested and applied. This concept is adequate to the time-domain model and reduces the computational demands. Several two-dimensional simulations allowed to isolate the individual effects of wind and screen on the propagation of 500 Hz sound waves over a 4-m high noise barrier. At a distance of 250 m from the source (240 m behind the screen) the sheltering effect of the screen and the refraction effect of the wind are in the order of 6 and 4 dB, respectively. The screen-induced turbulence leads to fluctuations in the noise level with a standard deviation of 1.2 dB and a maximum amplitude of 3 dB. However, the time averaged effect turned out to be in the order of merely 0.2 dB. The effect of the screen-induced turbulence on the average noise level behind the screen is therefore negligible.     

Quenched asymptotics of the ground state energy of random Schrödinger operators with scaled Gibbsian potentials

 This article describes the almost sure infinite volume asymptotics of the ground state energy of random Schr?dinger operators with scaled Gibbsian potentials. The random potential is obtained by distributing soft obstacles according to an infinite volume grand canonical tempered Gibbs measure with a superstable pair interaction. There is no restriction on the strength of the pair interaction: it may be taken, e.g., at a critical point. The potential is scaled with the box size in a critical way, i.e. the scale is determined by the typical size of large deviations in the Gibbsian cloud. The almost sure infinite volume asymptotics of the ground state energy is described in terms of two equivalent deterministic variational principles involving only thermodynamic quantities. The qualitative behaviour of the ground state energy asymptotics is analysed: Depending on the dimension and on the H?lder exponents of the free energy density, it is identified which cases lead to a phase transition of the asymptotic behaviour of the ground state energy. Received: 24 June 2002 / Revised version: 17 February 2003 Published online: 12 May 2003 Mathematics Subject Classification (2000): Primary 82B44; Secondary 60K35 Key words or phrases: Gibbs measure – H?lder exponents – Random Schr?dinger operator – Ground state – Large deviations     

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.