Topology optimization methods for guided flow – comparison of optimality criteria vs. phase-field method

Optimization of guided flow problems is an important task for industrial applications especially those with high Reynolds numbers. There exist several optimization methods to increase the energy efficiency of these problems. Different optimization methods are shown bei Klimetzek [1], Hinterberger [2] and Pingen [3]. In recent years the phase-field method has been shown to be an applicable method for different kinds of topology optimization [4, 5]. We present results of topology optimization methods with optimality criterion and by using a phase-field model in the area of guided fluid flow problems. The two methods aim on the same main target reducing the pressure drop between the inlet and outlet of the flow domain. The first method is based on local optimality criterion, preventing the backflow in the flow domain [1, 6, 7]. The second method is based on a phase field model, which describes a minimization problem and uses a specially constructed driving force to minimize the total energy of the system [4, 5]. We investigate the capabilities and limits of both methods and present examples of different resulting geometries. The initial configurations are prepared in a way that the same optimization problem is solved with both methods. We discuss these results regarding the shape of the improved flow geometry. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Differential activation of the lateral premotor cortex during action observation

Background  

Action observation leads to neural activation of the human premotor cortex. This study examined how the level of motor expertise (expert vs. novice) in ballroom dancing and the visual viewpoint (internal vs. external viewpoint) influence this activation within different parts of this area of the brain.     

Characterisation of poly(ethylene oxide) sulfonic acids

PEO sulfonic acids with M_w in the range 446–4246 have been prepared. Mechanically stable polyelectrolyte films containing high molar mass PEO and PEO sulfonic acids were prepared. The PEO sulfonic acids and the polyelectrolyte films were examined by thermal analysis, optical microscopy, Raman spectroscopy, and impedance spectroscopy. While the low molar mass PEO sulfonic acids were completely amorphous, sulfonic acids with M_w ≥ 1246 show considerable crystallinity. Experimental data indicate aggregation of the low molar mass PEO sulfonic acids through hydrogen bonds. The PEO sulfonic acids are miscible with high molar mass PEO and form free standing polyelectrolyte films. The PEO sulfonic acids with the lowest molar masses have a plasticizing effect on the high molar mass PEO. The crystallinity of the films decreased as the concentration of sulfonic acid increased. The films are stable at RH ≤ 75%, and for some mixtures protonic conductivities of 10⁻³ S cm⁻¹ at room temperature were reached.     

The McKay conjecture for exceptional groups and odd primes

Let G be a simply-connected simple algebraic group over an algebraically closed field of characteristic p with a Frobenius map F : G → G and G := G ^F , such that the root system is of exceptional type or G is a Suzuki group or Steinberg’s triality group. We show that all irreducible characters of C _G (S), the centraliser of S in G, extend to their inertia group in N _G (S), where S is any F-stable Sylow torus of (G, F). Together with the work in [16] this implies that the McKay conjecture is true for G and odd primes ℓ different from the defining characteristic. Moreover it shows important properties of the associated simple groups, which are relevant for the proof that the associated simple groups are good in the sense of Isaacs, Malle and Navarro, as defined in [14]. This research has been supported by the DFG-grant “Die Alperin-McKay-Vermutung für endliche Gruppen” and an Oberwolfach Leibniz fellowship.