Abel Symposia

Discrete Morse theory has recently lead to new developments in the theory of random geometric complexes. This article surveys the methods and results obtained with this new approach, and discusses some of its shortcomings. It uses simulations to illustrate the results and to form conjectures, getting numerical estimates for combinatorial, topological, and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics

Random tessellations and Boolean random functions

Abstract. Generalizations of various random tessellation models generated by Poisson point processes are proposed and their functional probability P (K) is given. They are interpreted as characteristics of Boolean random functions models, which provide a generic way of simulation of general random tessellations

Anisotropy analysis of pressed point processes

This paper introduces methods for the detection of anisotropies which are caused by compression of regular three-dimensional point patterns. Isotropy tests based on directional summary statistics and estimators for the compression factor are developed. These allow not only for the detection of anisotropies but also for the estimation of their strength. Using simulated data the power of the methods and the dependence of the power on the intensity, the degree of regularity, and the compression strength are studied. The motivation of this paper is the investigation of anisotropies in the structure of polar ice. Therefore, our methods are applied to the point patterns of centres of air pores extracted from tomographic images of ice cores. This way the presence of anisotropies in the ice caused by the compression of the ice sheet as well as an increase of their strength with increasing depth are shown

Evidence of second order transition induced by the porosity in the thermal conductivity of sintered metals

International audienceIn this paper, using both experimental data and theoretical modelling, we investigate the degradation of the thermal conductivity of sintered metals due simultaneously to the grain boundary thermal resistance and the porosity. We show that the porosity dependence of the thermal conductivity of sintered material from spherical particle powder, exhibits a critical behaviour associated with a second order phase transition. An analytical model with a single parameter is proposed to describe the critical behaviour of the thermal conductivity of sintered metals versus porosity. (C) 2014 Author(s)

In situ demineralisation of human enamel studied by synchrotron based X ray microtomography A descriptive pilot study

An in situ study was designed to investigate naturally developed demineralisation in human enamel in a widely non destructive manner in combination with X ray microtomography. Samples of human enamel were carried in the oral cavity of participants for 24 h daily for either 21 or 29 days using so called intraoral mandibular appliances ICTs . Demineralisation was thereby generated in a natural way without causing caries in the subjects dentition. By employing synchrotron based X ray microtomography XMT in combination with volume image analysis, a quantification and three dimensional visualisation of different stages of mineral density loss was possible. Basic features of the demineralised samples were similar to those reported in earlier in vitro studies. However, the analysed samples showed significant differences in the morphology of surface attack and the degree of mineral density loss depending on the carrier, the exposure time and the position within the ICT. In particular, the varying local conditions within a carrier s oral cavity seem to be different than in an in vitro study. Our results show that the combination of ICTs and quantitative image analysis applied to XMT data provides an analytical tool which is highly suited for the fundamental investigation of naturally developed demineralisation processe