Two-constraint domain decomposition with Space Filling Curves

In scientific computing, Space Filling Curves are a widely used tool for one-constraint domain decomposition. They provide a mechanism to sort multi-dimensional data in a locality preserving way, and, in this way, a (one dimensional) list of mesh elements is established which is subsequently split into 3 partitions under consideration of the constraint. This procedure has a runtime of O(NlogN) (N is the number of mesh elements) while nearly perfect load balancing can be established with reasonable partition surface sizes.In this work, we discuss the extensibility of this procedure to two-constraint settings which is desirable, since the methodology is extremely fast. Here, the splitting operation is subject to two constraints, and, unlike to the one-constraint case, obtaining near perfect balancing is often hard to establish, and is, even more as in the one-constraint case, in conflict with the induced surface sizes (or edge-cuts). We discuss multiple strategies to tackle the splitting, and we present a fast, O(NlogN) splitting heuristic algorithm which provides an integer σ that allows to trade off between balancing and surface sizes which results in a O(NlogN) two-constraint decomposition method. Results are compared to the multi-constraint domain decomposition abilities implemented in the Metis software package, and show that the method produces higher surface sizes, but is orders of magnitudes faster which makes the method superior for certain applications.     

Preparation of Ring-Shaped Thermoelectric Legs from PbTe Powders for Tubular Thermoelectric Modules

Waste heat recovery—for example, in automotive applications—is a major field for thermoelectric research and future application. Commercially available thermoelectric modules are based on planar structures, whereas tubular modules may have advantages for integration and performance in the field of automotive waste heat recovery. One major drawback of tubular generator designs is the necessity for ring-shaped legs made from thermoelectric material. Cutting these geometries from sintered tablets leads to considerable loss of thermoelectric material and therefore high cost. Direct sintering of ring-shaped legs or tubes of thermoelectric material is a solution to this problem. However, sintering such rings with high homogeneity and density faces some difficulties related to the mechanical properties of typical thermoelectric materials such as lead telluride (PbTe)—particularly brittleness and high coefficient of thermal expansion. This work shows a process for production of thermoelectric rings made of p- and n-doped PbTe. Long tubes of PbTe have been sintered in a current-assisted sintering process with specially designed sintering molds, coated with a diffusion barrier, and finally cut into ring-shaped slices. To demonstrate the technology, a tubular thermoelectric module has been assembled using these PbTe rings.     

Reactive and stimuli-responsive maleic anhydride containing macromers – multi-functional cross-linkers and building blocks for hydrogel fabrication

Macromers with functional groups that allow for chemical derivatization, polymerization reactions or impart specific physico-chemical properties are functional building blocks for polymeric systems used in different biomedical applications. With this motivation, a series of oligomeric macromers was synthesized by free radical polymerization of maleic anhydride (MA) with N-isopropylacrylamide (NiPAAm) and pentaerythritol diacrylate monostearate (PEDAS). This chemical design provides anhydride groups for effective reactivity of the macromers with amines and other nucleophiles, copolymerized NiPAAm for temperature responsiveness and lipophilic stearate domains for increased hydrogel stability. Macromers were synthesized with different MA co-monomer feeds and oligomeric molecules (Mn below 5000 Da) were obtained with MA contents between 7% and 27% as determined by titration. The fraction of chemically intact anhydrides was calculated to range from 75% to 80%. The ability of the macromers to cross-link di- or oligovalent amines as a function of MA content was investigated rheologically. It was also demonstrated that monovalent amines, e.g. aminofluorescein, could be grafted to the macromer chain utilizing only a fraction of the anhydride functionalities. The derivatized macromers could still participate in cross-linking reactions due to the remaining anhydrides. Temperature sensitivity was shown for aqueous solutions of macromers with fully dissociated anhydride groups. The solutions were additionally responsive to changes in calcium ion concentration and pH. Extracts from macromer cross-linked polyether hydrogels showed no toxicity on L929 fibroblasts.The macromers have perspective as biocompatible cross-linkers for hydrogel fabrication from various biomacromolecules with the opportunity to decorate the gels with monoamine molecules that alter the biological or physico-chemical properties.     

Hydrogen storage in bulk Mg-Ti and Mg-stainless steel multilayer composites synthesized via accumulative roll-bonding (ARB)

We have tested the hydrogen storage cycling behavior of bulk centimeter-scale magnesium - titanium and magnesium - stainless steel multilayer composites synthesized by accumulative roll-bonding (ARB). Roll-bonding of either titanium or stainless steel with magnesium allows the reversible hydrogen sorption of the resulting composite at 350 °C. Identically roll-bonded pure magnesium can hardly be absorbed at this temperature. In the composites, the kinetics of the first cycle of absorption (also called “activation”) improves with increased number of fold and roll (FR) operations. With increasing FR operations the distribution of the Ti phase is progressively refined, and the shape of the absorption curve no longer remains sigmoidal. Increasing the loading amount of the second phase also accelerates the kinetics. This holds true up to a threshold limit. Microscopy analysis performed on 1-2 wt.% hydrogen absorbed composites demonstrates that MgH₂ formed exclusively on various heterogeneous nucleation sites. During activation, MgH₂ nucleation occurred at the Mg-hard phase interfaces. During the subsequent absorption cycles, heterogeneous nucleation primarily occurred in the vicinity of “internal” free surfaces such as cracks.     

Identification and kinetics of oxidized compounds from phosphatidylcholine molecular species

Heat-induced oxidative modifications of two phosphatidylcholine molecular species as potential functional food components were evaluated. 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine (SOPC) and 1-stearoyl-2-linoleoyl-sn-glycero-3-phosphocholine (SLPC) were chosen as models. The optimal temperature for hydroperoxide formation was determined by MS for each standard: 125 °C for SLPC and 150 °C for SOPC. Oxidation was performed at these temperatures and degradation products were identified using LC–ESI-MS combined to an acid treatment. Kinetics of formation of oxidation products from SOPC and SLPC were monitored over 120 min and curves were drawn for each identified structure. Results showed that native phospholipids rapidly decreased with heat and that oxidation products showed functions, such as hydroxyl, oxo or epoxy groups. Kinetics pointed out that some of these quite stable oxidation products are likely to be found in sizable amounts in processed foods containing phospholipids.     

Equivalence Problems for Circuits over Sets of Natural Numbers

We investigate the complexity of equivalence problems for {∪,∩,⁻,+,×}-circuits computing sets of natural numbers. These problems were first introduced by Stockmeyer and Meyer (1973). We continue this line of research and give a systematic characterization of the complexity of equivalence problems over sets of natural numbers. Our work shows that equivalence problems capture a wide range of complexity classes like NL, C ₌ L, P,Π₂^P, PSPACE, NEXP, and beyond. McKenzie and Wagner (2003) studied related membership problems for circuits over sets of natural numbers. Our results also have consequences for these membership problems: We provide an improved upper bound for the case of {∪,∩,⁻,+,×}-circuits.