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Das Spiel mit dem Raum : Materialien zu einem entwicklungsorientierten Kunstunterricht, 3. Teil
(1994)
Das Spiel mit der Farbe : Materialien zu einem entwicklungsorientierten Kunstunterricht, 4. Teil
(1994)
Angelova, Angelina ; Penacorada, Florencio ; Stiller, Burkhard ; Zetzsche, Thomas ; Ionov, Radoslav ; Kamusewitz, Helmut ; Brehmer, Ludwig
Angelova, Angelina ; Reiche, Jürgen ; Ionov, Radoslav ; Janietz, Dietmar ; Lemmetyinen, Helge ; Brehmer, Ludwig
Changes of the molecular arrangenemt that can be induced by means of the LB technique in the multilayers of a disc-shaped multialkynyl amphiphile are monitored by means of small angle X-ray diffraction. Studies of the monolayers at the air-water interface reveal "edge-on" orientation of the discs. Specific effects of the counter- ions (Na+, Cd²+, Pb²+, and Ba²+) and sub-solution pH on the monolayer collapse pressure, transfer efficiency and molecular order in the multilayers are found. A correlation between the monolayer properties and the ability for formation of periodic discotic structures in the presence of divalent counterions is established. The discotic molecules retain their "edge-on" arrangement in the highly compressed transferred films with slight irregular interdigtation of the flexible wings and inclination to the substrate normal. The tilt and the inter- digitation are reduced when the discotic monolayers are deposited in alternating LB films with barium arachidate spacer layers.
Solubilization by polysoaps
(1994)
The aqueous solubilization power of several series of micellar homopolymers and copolymers (polysoaps) is investigated. Using five insoluble or poorly water-soluble dyes, comparisons of the capacities are made with respect ot the influence of structural variables such as the polymer backbone, the polymer geometry, the comonomer content, and the charge of the hydrophilic group. Some guidelines for polysoap structures suited for efficient solubilization are established. Noteworthy is that the solubilization capacities of the polysoaps are neither linked to the ability to reduce the surface tension of water, nor to the polarity of the solubilization sites deduced from spectroscopic probes.
Many methods have been proposed for the simulation of constrained mechanical systems. The most obvious of these have mild instabilities and drift problems. Consequently, stabilization techniques have been proposed A popular stabilization method is Baumgarte's technique, but the choice of parameters to make it robust has been unclear in practice. Some of the simulation methods that have been proposed and used in computations are reviewed here, from a stability point of view. This involves concepts of differential-algebraic equation (DAE) and ordinary differential equation (ODE) invariants. An explanation of the difficulties that may be encountered using Baumgarte's method is given, and a discussion of why a further quest for better parameter values for this method will always remain frustrating is presented. It is then shown how Baumgarte's method can be improved. An efficient stabilization technique is proposed, which may employ explicit ODE solvers in case of nonstiff or highly oscillatory problems and which relates to coordinate projection methods. Examples of a two-link planar robotic arm and a squeezing mechanism illustrate the effectiveness of this new stabilization method.
Many methods have been proposed for the stabilization of higher index differential-algebraic equations (DAEs). Such methods often involve constraint differentiation and problem stabilization, thus obtaining a stabilized index reduction. A popular method is Baumgarte stabilization, but the choice of parameters to make it robust is unclear in practice. Here we explain why the Baumgarte method may run into trouble. We then show how to improve it. We further develop a unifying theory for stabilization methods which includes many of the various techniques proposed in the literature. Our approach is to (i) consider stabilization of ODEs with invariants, (ii) discretize the stabilizing term in a simple way, generally different from the ODE discretization, and (iii) use orthogonal projections whenever possible. The best methods thus obtained are related to methods of coordinate projection. We discuss them and make concrete algorithmic suggestions.