A short and versatile finite element multiscale code for homogenization problems

We describe a multiscale finite element (FE) solver for elliptic or parabolic problems with highly oscillating coefficients. Based on recent developments of the so-called heterogeneous multiscale method (HMM), the algorithm relies on coupled macro- and microsolvers. The framework of the HMM allows to design a code whose structure follows the classical finite elements implementation at the macro level. To account for the fine scales of the problem, elementwise numerical integration is replaced by micro FE methods on sampling domains. We discuss a short and flexible FE implementation of the multiscale algorithm, which can accommodate simplicial or quadrilateral FE and various coupling conditions for the constrained micro simulations. Extensive numerical examples including three dimensional and time dependent problems are presented illustrating the efficiency and the versatility of the computational strategy.     

High‐Temperature Creep Behavior of Dense SiOC‐Based Ceramic Nanocomposites: Microstructural and Phase Composition Effects

In this work, dense monolithic polymer‐derived ceramic nanocomposites (SiOC, SiZrOC, and SiHfOC) were synthesized via hot‐pressing techniques and were evaluated with respect to their compression creep behavior at temperatures beyond 1000°C. The creep rates, stress exponents as well as activation energies were determined. The high‐temperature creep in all materials has been shown to rely on viscous flow. In the quaternary materials (i.e., SiZrOC and SiHfOC), higher creep rates and activation energies were determined as compared to those of monolithic SiOC. The increase in the creep rates upon modification of SiOC with Zr/Hf relies on the significant decrease in the volume fraction of segregated carbon; whereas the increase of the activation energies corresponds to an increase of the size of the silica nanodomains upon Zr/Hf modification. Within this context, a model is proposed, which correlates the phase composition as well as network architecture of the investigated samples with their creep behavior and agrees well with the experimentally determined data.     

Killing Me Softly—Future Challenges in Apoptosis Research

The induction of apoptosis, a highly regulated and clearly defined mode of cell dying, is a vital tenet of modern cancer therapy. In this review we focus on three aspects of apoptosis research which we believe are the most crucial and most exciting areas currently investigated and that will need to be better understood in order to enhance the efficacy of therapeutic measures. First, we discuss which target to select for cancer therapy and argue that not the cancer cell as such, but its interaction with the microenvironment is a more promising and genetically stable site of attack. Second, the complexity of combination therapy is elucidated using the PI3-K-mediated signaling network as a specific example. Here we show that the current clinical approach to sensitize malignancies to apoptosis by maximal, prolonged inhibition of so-called survival pathways can actually be counter productive. Third, we propose that under certain conditions which will need to be clearly defined in future, chronification of a tumor might be preferable to the attempt at a cure. Finally, we discuss further problems with utilizing apoptosis induction in cancer therapy and propose a novel potential therapeutic approach that combines the previously discussed features.     

Phase separation of a hafnium alkoxide-modified polysilazane upon polymer-to-ceramic transformation—A case study

The polymer-to-ceramic transformation of a hafnium alkoxide-modified polysilazane was investigated via thermogravimetric analysis coupled with in situ mass spectrometry (TG/MS), nuclear magnetic resonance (MAS NMR) and transmission electron microscopy (TEM). The results indicate that the structural evolution of the polysilazane upon ceramization is strongly affected by the modification with hafnium alkoxide. Thus, the content of carbon in the ceramic backbone was relatively low, whereas a large amount of SiN₄ sites and a segregated carbon phase was present in the sample. Furthermore, this study revealed the formation of a SiHfCNO amorphous single phase ceramic via pyrolysis of the polymer at 700 °C, whereas at higher pyrolysis temperatures precipitation of hafnia was observed, leading to an amorphous hafnia/silicon carbonitride ceramic nanocomposite. The precipitation of hafnia was shown to not rely on decomposition processes, but to be a result of rearrangement reactions occurring within the ceramic material.     

Stability Behavior of Liquid Jets under Gravity

The influence of gravity on the stability behavior of falling liquid strands without external excitation was investigated. To this end, a mathematic‐physical model was developed for the analysis of the stability behavior of liquid strands in the range of low to higher viscosity, the main emphasis being on gravity. The characteristics of the model are discussed and, finally, the stability criterion is derived for the quantitative determination of the point of disintegration.     

Strong influence of polymer architecture on the microstructural evolution of hafnium-alkoxide-modified silazanes upon ceramization

The present study focuses on the synthesis and ceramization of novel hafnium-alkoxide-modified silazanes as well as on their microstructure evolution at high temperatures. The synthesis of hafnia-modified polymer-derived SiCN ceramic nanocomposites is performed via chemical modification of a polysilazane and of a cyclotrisilazane, followed by cross-linking and pyrolysis in argon atmosphere. Spectroscopic investigation (i.e., NMR, FTIR, and Raman) shows that the hafnium alkoxide reacts with the N-H groups of the cyclotrisilazane; in the case of polysilazane, reactions of N-H as well as Si-H groups with the alkoxide are observed. Consequently, scanning and transmission electron microscopy studies reveal that the ceramic nanocomposites obtained from cyclotrisilazane and polysilazane exhibited markedly different microstructures, which is a result of the different reaction pathways of the hafnium alkoxide with cyclotrisilazane and with polysilazane. Furthermore, the two prepared ceramic nanocomposites are unexpectedly found to exhibit extremely different high-temperature behavior with respect to decomposition and crystallization; this essential difference is found to be related to the different distribution of hafnium throughout the ceramic network in the two samples. Thus, the homogeneous distribution of hafnium observed in the polysilazane-derived ceramic leads to an enhanced thermal stability with respect to decomposition, whereas the local enrichment of hafnium within the matrix of the cyclotrisilazane-based sample induces a pronounced decomposition upon annealing at high temperatures. The results indicate that the chemistry and architecture of the precursor has a crucial effect on the microstructure of the resulting ceramic material and consequently on its high-temperature behavior.     

Bandwidth-allocation policies for unicast and multicast flows

Using multicast delivery to multiple receivers reduces the aggregate bandwidth required from the network compared to using unicast delivery to each receiver. However, multicast is not yet widely deployed in the Internet. One reason is the lack of incentive to use multicast delivery. To encourage the use of multicast delivery, we define a new bandwidth-allocation policy, called LogRD, taking into account the number of downstream receivers. This policy gives more bandwidth to a multicast flow as compared to a unicast flow that shares the same bottleneck, without starving the unicast flows, however. The LogRD policy also provides an answer to the question on how to treat a multicast flow compared to a unicast flow sharing the same bottleneck. We investigate three bandwidth-allocation policies for multicast flows and evaluate their impact on both receiver satisfaction and fairness using a simple analytical study and a comprehensive set of simulations. The policy that allocates the available bandwidth as a logarithmic function of the number of receivers downstream of the bottleneck achieves the best tradeoff between receiver satisfaction and fairness     

Adaptive finite element heterogeneous multiscale method for homogenization problems

In this paper we present an a posteriori error analysis for elliptic homogenization problems discretized by the finite element heterogeneous multiscale method. Unlike standard finite element methods, our discretization scheme relies on macro- and microfinite elements. The desired macroscopic solution is obtained by a suitable averaging procedure based on microscopic data. As the macroscopic data (such as the macroscopic diffusion tensor) are not available beforehand, appropriate error indicators have to be defined for designing adaptive methods. We show that such indicators based only on the available macro- and microsolutions (used to compute the actual macrosolution) can be defined, allowing for a macroscopic mesh refinement strategy which is both reliable and efficient. The corresponding a posteriori estimates for the upper and lower bound are derived in the energy norm. In the case of a uniformly oscillating tensor, we recover the standard residual-based a posteriori error estimate for the finite element method applied to the homogenized problem. Numerical experiments confirm the efficiency and reliability of the adaptive multiscale method.