On dimension-free Sobolev imbeddings I

We prove dimension-invariant imbedding theorems for Sobolev spaces using the Gross logarithmic inequality.     

Modeling Unsaturated Flow in Absorbent Swelling Porous Media: Part 1. Theory

The flow and deformation processes in swelling porous media are modeled for absorbent hygiene products (e.g., diapers, wipes, papers etc.). The first part of the article derives the fundamental equations for the hysteretic unsaturated flow, liquid absorption, and large deformation. The final set of model equations consists of balance equations of mobile and absorbed (immobile) liquid combined with a series of constitutive relationships. The resulting equation system is strongly nonlinear and requires advanced numerical strategies for solving. The second part of the article focuses on numerical solution and presents simulation results for 2D and 3D applications.     

Strong Static Stability of Liquid Layers

For a class of disjoining pressure potentials we show that liquid layers in equilibrium with positive second variation for nonvanishing variations (called stable by definition) are in fact strong minimizers of the associated energy functional. In a previous paper, explicit stable layers are obtained for some cases of solid configurations with simple geometries, in particular for a single cylindrical or spherical cavity. From this note it follows that all these “stable” equilibria are strong energy minimizers. No smallness for the thickness of the layer is assumed.     

Permethylcyclohexane

Permethylcyclohexane 2 has been synthesized and investigated by dynamic NMR spectroscopy. An unexpectedly low barrier (ΔG3₃₃₃ = 70.0 kJ/mol) of its chair-to-chair interconversion was found.     

Kontrahierbare analytische Algebren

Ohne Zusammenfassung     

Solutions of the anti-self-dualSU(2) Yang-Mills equations gained from the inverse scattering method

By applying the inverse scattering method in connection with a dressing procedure a huge class of solutions of the anti-self-dualSU(2) Yang-Mills equation is obtained. This class contains also the well-known't Hooft instantions.