Rheological analysis of triblock copolymer-microemulsion networks

The rheological properties of microemulsion-triblock copolymer [poly(oxyethylene)-b-polyisoprene-b-poly(oxyethylene)] networks were studied by oscillatory shear measurements. The principal viscoelastic pattern of our systems stays the same whether the surfactant is ionic or nonionic. A closer examination shows, however, the enormous influence of the respective phase behavior of the underlying microemulsions. Also, specific interactions between the surfactants and the hydrophilic poly(oxyethylene) blocks lead to a significant effect on the formation of network structures.Characteristic rheological data such as plateau moduli and relaxation times for a series of different samples were derived differing in polymer or droplet concentrations, apart from the molecular weights of the poly-(oxyethylene) and the polyisoprene blocks. Finally, we could construct polymer and droplet concentration invariant master — mastercurves using the temperature invariant mastercurves.     

Fast Legendre spectral method for computing the perturbation of a gradient temperature field in an unbounded region due to the presence of two spheres

The temperature distribution around two spheres is considered when the main field has a constant gradient at infinity. Bispherical coordinates are used, together with a transformation of the dependent variable that leads to separation of variables. Then the solution can be sought in Legendre series with respect to one of the bispherical coordinates. An important element of the proposed work is the effective way to reduce an essentially 3D problem to a set of three 2D problems. The Legendre spectral method is shown to have an exponential convergence which is confirmed by the computations. The efficiency is so high that even for the hard cases of two closely situated spheres, an accuracy of 10^?10 is achieved with as few as 20 terms in the expansion. Solutions with both longitudinal and transverse gradients at infinity are obtained, and the contour lines of the temperature field are presented graphically. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

On the Stability of the O(N)-Invariant and the Cubic-Invariant Three-Dimensional N-Component Renormalization-Group Fixed Points in the Hierarchical Approximation

We compute renormalization-group fixed points and their spectrum in an ultralocal approximation. We study a case of two competing nontrivial fixed points for a three-dimensional real N-component field: the O(N)-invariant fixed point vs. the cubic-invariant fixed point. We compute the critical value N _c of the cubic ⁴-perturbation at the O(N)-fixed point. The O(N)-fixed point is stable under a cubic ⁴-perturbation below N _c; above N _c it is unstable. The Critical value comes out as 2.219435<N _c<2.219436 in the ultralocal approximation. We also compute the critical value of N at the cubic invariant fixed point. Within the accuracy of our computations, the two values coincide.     

Über die Assoziation des Wassers an gespreiteten Alkylcarbonsäurefilmen

Summary Especially the liquid expanded state of spread monolayers of insoluble saturated carboxylic acids on water at different temperatures is investigated. It was found thermodynamically, that this state occurs by orientated adsorption of four respectively of five water molecules on the COOH-group. These molecules will be adsorbed by extension of the film covered surface and desorbed by compression of the film. The monolayers are always in a state, which gives the layer material properties very different from the properties in the bulk state. The behavior of the surface film, or, what is the same, of the surface solution, is that of a special substance with an own critical temperature, critical pressure and a two dimensional critical volume. These facts are very important, they influence the density, the refraction index, the dipol moment and other properties of adsorbed molecules.It is also a state-equation derived and the energies for adsorption and desorption are calculated and a formula for predicting the course of force-/area-isotherms of spread carboxylic acid monolayers in dependence of the temperature is also derived. Thereby was found a new confirmation for the rule ofAdam.

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Herrn Prof. Dr.Otto Bayer zum 70. Geburtstag gewidmet.     

Die Algebra des Isotopen Spins (3/2, 1/2)

Zusammenfassung Alle irreduziblen Systeme von n hermitischen Matrizen _j, die den zyklischen Vertauschungsrelationen dritten Grades (s. Gl. (14)) genügen, werden explizite aufgefunden. Es zeigt sich insbesondere, dass bei n=3nur zwei solche nichttriviale Lösungen existieren, eine sechsreihige und eine vierreihige. Die erste ist mit dem von Votruba und Lokajíek zwecks Beschreibung des Verhaltens des isotopen Spins des Nukleons eingeführten Matrixsystem äquivalent. Die zweite Lösung erfüllt zugleich auch die Kemmerschen Relationen. Für jedes n>3gibt es nur je eine nichttriviale Lösung, nämlich die Kemmersche von der Ordnung N=n+1.     

Parity violation in SLAC experiment and left-right symmetric gauge models

It is shown that the left-right symmetric gauge models based on the group $\text{G}$ = SU(2)_L × SU(2)_R × U(1)_L × U(1)_R can accommodate quite naturally the results of the recent SLAC experiment concerning parity violation in neutral currents. The possibility of finding a light neutral gauge boson in the PETRA-PEP energy range remains particularly interesting.