An EKR-theorem for finite buildings of type $$D_{\ell }$$

We define optimal EKR-sets in finite buildings. This definition is motivated by various contributions on optimal EKR-sets in finite projective spaces and polar spaces. Our main result is the classification of optimal EKR-sets of type \(\{ \ell , \ell -1\}\) in finite building of type \(D_{\ell }\) with \(\ell \) even. As it is the case for most of the known optimal EKR-sets in finite buildings, our EKR-sets have a natural center. This provides some evidence that the EKR-problem for finite buildings and Tits center conjecture are closely related.     

Miklós–Manickam–Singhi conjectures on partial geometries

In this paper we give a proof of the Miklós–Manickam–Singhi (MMS) conjecture for some partial geometries. Specifically, we give a condition on partial geometries which implies that the MMS conjecture holds. Further, several specific partial geometries that are counterexamples to the conjecture are described.     

Efficient charge transport along phenylene-vinylene molecular wires

We have studied the motion of charge carriers along isolated phenylene-vinylene (PV) chains using a combination of experimental and theoretical methods. The conductive properties of positive charges along PV chains in dilute solution were studied by using the pulse-radiolysis time-resolved microwave conductivity (TRMC) technique. This technique enables the measurement of high-frequency (tens of GHz) charge carrier mobilities along isolated PV chains without the use of electrodes. The charge carrier mobility along PV chains with finite and infinite length was studied theoretically by charge transport simulations with parameters from density functional theory (DFT) calculations. The high-frequency charge carrier mobility is found to depend strongly on the conjugation length of the PV chains and is found to increase both with increasing length of the PV chain and with increasing conjugation fraction. The experimental results are in good agreement with the calculated results. On the basis of this combined experimental and theoretical study an intrachain charge carrier mobility of a few tens of cm2/Vs is expected for an infinitely long PV chain without conjugation breaks.     

A Multiphasic Model Describing the CO2 Injection Problem

According to the annual data, the portion of ejected carbon dioxide (CO₂) into the atmosphere is much higher in comparison to other greenhouse gases. Therefore, the development of various scenarios in order to reduce the CO₂ concentration in the atmosphere is nowadays a challenge and a relevant subject in research. The current investigation is dedicated to the modelling of a CO₂ injection into a water-saturated aquifer as the most capable reservoir, where its upward migration is blocked by a dense cap-rock layer. The major part of the study is focused on two specific processes taking place in the stored reservoir: the phase transfer phenomenon of the supercritical CO₂ which occurs under changeable surrounding conditions and the sequestration-driven deformation of the solid skeleton acting under the pressure of the pumped CO₂. For the numerical simulations within a continuum-mechanical framework, a multiphasic model based on the Theory of Porous Media is introduced. Moreover, the main principles of developing a constitutive equation for the mass production term for the mass balance equation are discussed here. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Particle simulation of granular media and homogenisation towards continuum quantities

From a microscopic point of view, various natural and engineering materials consist of individual grains, whose motion strongly influence the macroscopic material behaviour. Exemplarily, one may look at the development of shear zones in natural granular materials, such as sand, occurring as a result of local grain dislocations and the transition of the granulate from a denser to a looser packing. The intuitive modelling approach for granular assemblies is consequently the consideration of each grain as a rigid particle. In a numerical framework, this leads to the Discrete Element Method (DEM), wherein the motion of each particle can be obtained solving Newton's equations for each particle. The present contribution discusses the basic fundaments of modelling granular material on the microscopic scale by use of the DEM. Special interest is taken to the constitutive choice of the governing particle-to-particle contact forces, as they have to account for plastic material behaviour as well as for assumptions concerning particle shape, size and distribution. As engineering problems are regularly described on the macroscale by means of continuum mechanics, a homogenisation strategy transfers the information from the microscale towards continuum quantities via volume averaging. Therefore, characteristic Representative Elementary Volumes (REV) are constructed by an ensemble of particles, where each particle can be chosen as the centre of a REV. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)