Shape-Aware Matching of Implicit Surfaces Based on Thin Shell Energies

A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane energy measuring the rate of tangential distortion when deforming the reference shell into the template shell, and a bending energy measuring the bending under the deformation in terms of the change of the shape operators from the undeformed into the deformed configuration. The variational method applies to surfaces described as level sets. It is mathematically well-posed, and an existence proof of an optimal matching deformation is given. The variational model is implemented using a finite element discretization combined with a narrow band approach on an efficient hierarchical grid structure. For the optimization, a regularized nonlinear conjugate gradient scheme and a cascadic multilevel strategy are used. The features of the proposed approach are studied for synthetic test cases and a collection of geometry processing examples.     

Influence of the aluminum alkyl co-catalyst type in Ziegler-Natta ethene polymerization on the formation of active sites, polymerization rate, and molecular weight

The influence of the concentration of the co-catalysts triethylaluminium (TEAL), tri-iso-butylaluminium (TIBAL), tri-n-octylaluminium on the polymerization rate for standard Ziegler-Natta catalyst systems was studied. By comparing the influence of monomeric TIBAL with TEAL co-catalyst on the polymerization activity, the effect of TEAL dimerization was described. The use of the Eley-Ridealadsorption model instead of Langmuir-Hinselwood model is proposed for the absorption of monomeric aluminiumalkyl species and for the formation of active centers C*. It is further proposed that steric hindrance from different co-catalysts, which results in a higher molecular weight (MW) of polymers, is caused by active centers with reduced space for chain transfer reactions.     

Numerical methods for the simulation of a coalescence-driven droplet size distribution

The droplet size distribution in a turbulent flow field is considered and modeled by means of a population balance system. This paper studies different numerical methods for the 4D population balance equation and their impact on an output of interest, the time-space-averaged droplet size distribution at the outlet, which is known from experiments. These methods include different interpolations of the experimental data at the inlet, various discretizations in time and space, and different schemes for computing the coalescence integrals. It will be shown that noticeable changes in the output of interest might occur. In addition, the computational efficiency of the studied methods is discussed.