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We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With numerical simulations that mimic typical experimental situations, we have identified an important constraint when characterizing such networks: indications of a small-world topology can be expected solely due to the spatial sampling of the system along with the commonly used time series analysis based approaches to network characterization.
Recently, we introduced and mathematically analysed a new method for grid deformation (Grajewski et al., 2009) [15] we call basic deformation method (BDM) here. It generalises the method proposed by Liao et al. (Bochev et al., 1996; Cai et al., 2004; Liao and Anderson, 1992) [4], [6], [20]. In this article, we employ the BDM as core of a new multilevel deformation method (MDM) which leads to vast improvements regarding robustness, accuracy and speed. We achieve this by splitting up the deformation process in a sequence of easier subproblems and by exploiting grid hierarchy. Being of optimal asymptotic complexity, we experience speed-ups up to a factor of 15 in our test cases compared to the BDM. This gives our MDM the potential for tackling large grids and time-dependent problems, where possibly the grid must be dynamically deformed once per time step according to the user's needs. Moreover, we elaborate on implementational aspects, in particular efficient grid searching, which is a key ingredient of the BDM.
Self metathesis of oleochemicals offers a variety of bifunctional compounds, that can be used as monomer for polymer production. Many precursors are in huge scales available, like oleic acid ester (biodiesel), oleyl alcohol (tensides), oleyl amines (tensides, lubricants). We show several ways to produce and separate and purify C18-α,ω-bifunctional compounds, using Grubbs 2nd Generation catalysts, starting from technical grade educts.
Metathese von Ölsäure und Derivaten ist ein interessanter Weg für die Synthese bifunktioneller Verbindungen aus nachwachsenden Rohstoffen. Verwendet wurden Ru-Katalysatoren der zweiten Generation, welche eine hohe Toleranz gegenüber funktionellen Gruppen und Verunreinigungen aufweisen. Trotz des Einsatzes technischer Edukte waren Umsetzungen mit niedrigen Katalysatormengen (0.001 – 0.01 mol-%) möglich, mit Ausbeuten entsprechend der Literatur. Kreuzmetathesen ermöglichten variable Kettenlängen und Funktionalitäten der Monomere, die Produktgewinnung ist jedoch aufwändig. Selbstmetathese lieferte C18-bifunktionelle Verbindungen, welche einfach durch Destillation oder Kristallisation isoliert werden können. Neben der katalystischen Umsetzung wurde auch die Produktgewinnung untersucht und für ausgewählte Produkte auch im größeren Maßstab durchgeführt.